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The results of application of the Cluster Channels Orthogonal Functions Method in combination with the R-matrix theory for calculating the cross-sections of the reactions induced by 6Li + 2H collisions are presented. As part of this work, first, very high lying resonances that have a decisive influence on the cross-sections of these reactions were identified. Second, for the first time in the framework of a theoretical study of nuclear reactions, to the cross-sections of all binary reactions pass through one and the same compound nucleus were computed using a consistent unified theoretical approach. The yield of sequential tripartition reactions is also a subject of this study. [ABSTRACT FROM AUTHOR]

Protonated hydrogen cyanide, HCNH+, is one of the most important molecules of interest in the astrophysical and astrochemical fields. This molecule not only plays the role of a reaction intermediary in various types of interstellar reactions but was also identified in Titan's upper atmosphere. The cross sections for the dissociative recombination (DR) and vibrational (de-)excitation (VE and VDE) of HCNH+ and its CNH 2 + isomer are computed using a theoretical approach based on a combination of the normal mode approximation for the vibrational states of the target ions and the UK R-matrix code to evaluate electron-ion scattering matrices for fixed geometries of ions. The theoretical convoluted DR cross section for HCNH+ agrees well with the experimental data and a previous study. It was also found that the DR of the CNH 2 + isomer is important, which suggests that this ion might be present in DR experiments of HCNH+. Moreover, the ab initio calculations performed on the H2CN+ isomer predict that this ion is a transition state. This result was confirmed by the study of the reaction path of the HCNH+ isomerization that was carried out by evaluating the intrinsic reaction coordinate (IRC). Finally, thermally averaged rate coefficients derived from the cross sections are provided for temperatures in the 10–10,000 K range. A comprehensive set of calculations is performed to assess the uncertainty of the obtained data. These results should help in modeling non-LTE spectra of HCNH+, taking into account the role of its most stable isomer, in various astrophysical environments. [ABSTRACT FROM AUTHOR]

We explore the algebraic structure of a particular ansatz of the Yang-Baxter equation (YBE), which is inspired by the Bethe Ansatz treatment of the asymmetric simple exclusion process spin-model. Various classes of Hamiltonian density arriving from the two types of R-matrices are found, which also appear as solutions of the constant YBE. We identify the idempotent and nilpotent categories of such constant R-matrices and perform a rank-1 numerical search for the lowest dimension. A summary of the final results reveals general non-Hermitian spin-1/2 chain models. [ABSTRACT FROM AUTHOR]

Let U q (g) denote the rational form of the quantized enveloping algebra associated to a complex simple Lie algebra g. Let λ be a nonzero dominant integral weight of g , and let V be the corresponding type 1 finite-dimensional irreducible representation of U q (g). Starting from this data, the R -matrix formalism for quantum groups outputs a Hopf algebra U R λ (g) defined in terms of a pair of generating matrices satisfying well-known quadratic matrix relations. In this paper, we prove that this Hopf algebra admits a Chevalley–Serre type presentation which can be recovered from that of U q (g) by adding a single invertible quantum Cartan element. We simultaneously establish that U R λ (g) can be realized as a Hopf subalgebra of the tensor product of the space of Laurent polynomials in a single variable with the quantized enveloping algebra associated to the lattice generated by the weights of V. The proofs of these results are based on a detailed analysis of the homogeneous components of the matrix equations and generating matrices defining U R λ (g) , with respect to a natural grading by the root lattice of g compatible with the weight space decomposition of End (V). [ABSTRACT FROM AUTHOR]

In 2001–2013 Derkachov and Manashov with coauthors obtained simple and natural expressions of R-matrices for the principal series of representations of the groups S L (2 , C) , S L (2 , R) , S L (n , C) , SO(1, n). The Yang–Baxter identities for these intertwining operators are kinds of multivariate hypergeometric transformations. Derivations of the identities are based on calculations "of physical level of rigor" with divergent integrals. Our purpose is a formal mathematical justification of these results. [ABSTRACT FROM AUTHOR]

We show that the same algebraic data that permit to construct the Lax pair and the r-matrix of an integrable non-linear σ-model in 1 + 1 dimensions can be also used for the construction of Lax pairs and of r-matrices of several other non-trivial integrable theories in 1 + 0 dimension. We call those new integrable theories the point particle E -models, we describe their structure and give their physical interpretation. We work out in detail the point particle E -modelsassociated to the bi-Yang–Baxter deformation of the SU(N) principal chiral model. In particular, for each complex flag manifold we thus obtain a two-parameter family of integrable models living on it. [ABSTRACT FROM AUTHOR]

With the aim of investigating the existence of an integrable elliptic deformation of strings on AdS3 × S3 × T4, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on AdS3 × S3 in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden U(1) symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed AdS3 × S3 × T4 light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions. [ABSTRACT FROM AUTHOR]

This paper considers the (negative) cyclic open–closed map O C - , which maps the cyclic homology of the Fukaya category of a symplectic manifold to its S 1 -equivariant quantum cohomology. We prove (under simplifying technical hypotheses) that this map respects the respective natural connections in the direction of the equivariant parameter. In the monotone setting this allows us to conclude that O C - intertwines the decomposition of the Fukaya category by eigenvalues of quantum cup product with the first Chern class, with the Hukuhara–Levelt–Turrittin decomposition of the quantum cohomology. We also explain how our results relate to the Givental–Teleman classification of semisimple cohomological field theories: in particular, how the R-matrix is related to O C - in the semisimple case; we also consider the non-semisimple case. [ABSTRACT FROM AUTHOR]

We study the category Osh of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. Motivated by the representation theory of the Borel subalgebra of a quantum affine algebra and by the relevance of quantum integrable systems in this context, we prove that tensor products of prefundamental modules with irreducible modules are either cyclic or cocyclic. This implies the existence and uniqueness of morphisms, the R-matrices, for such tensor products. We prove the R-matrices are polynomial in the spectral parameter, and we establish functional relations for the R-matrices. As applications, we prove the Jordan-Holder property in the category Osh. We also obtain a proof, uniform for any finite type, that any irreducible module factorizes through a truncated shifted Yangian. [ABSTRACT FROM AUTHOR]

Dissociative recombination of N 2 H + is explored in a two-step theoretical study. In a first step, a diatomic (1D) rough model with a frozen NN bond and frozen angles is adopted, in the framework of the multichannel quantum defect theory (MQDT). The importance of the indirect mechanism and of the bending mode is revealed, in spite of the disagreement between our cross section and the experimental one. In the second step, we use our recently elaborated 3D approach based on the normal mode approximation combined with R-matrix theory and MQDT. This approach results in satisfactory agreement with storage-ring measurements, significantly better at very low energy than the former calculations. [ABSTRACT FROM AUTHOR]

Based on work related to the R-matrix theory, we first abstract the Lax pairs proposed by Blaszak and Sergyeyev into a unified form. Then, a generalized zero-curvature equation expressed by the Poisson bracket is exhibited. As an application of this theory, a generalized (2+1)-dimensional integrable system is obtained, from which a resulting generalized Davey–Stewartson (DS) equation and a generalized Pavlov equation (gPe) are further obtained. Via the use of a nonisospectral zero-curvature-type equation, some (3+1) -dimensional integrable systems are produced. Next, we investigate the recursion operator of the gPe using an approach under the framework of the R-matrix theory. Furthermore, a type of solution for the resulting linearized equation of the gPe is produced by using its conserved densities. In addition, by applying a nonisospectral Lax pair, a (3+1)-dimensional integrable system is generated and reduced to a Boussinesq-type equation in which the recursion operators and the linearization are produced by using a Lie symmetry analysis; the resulting invertible mappings are presented as well. Finally, a Bäcklund transformation of the Boussinesq-type equation is constructed, which can be used to generate some exact solutions. [ABSTRACT FROM AUTHOR]

We introduce new classes of integrable models that exhibit a structure similar to that of flag vector spaces. We present their Hamiltonians, R-matrices and Bethe-ansatz solutions. These models have a new type of generalized graded algebra symmetry. [ABSTRACT FROM AUTHOR]

Lie subalgebras of L = g ((x)) × g [ x ] / x n g [ x ] , complementary to the diagonal embedding Δ of g [ [ x ] ] and Lagrangian with respect to some particular form, are in bijection with formal classical r-matrices and topological Lie bialgebra structures on the Lie algebra of formal power series g [ [ x ] ] . In this work we consider arbitrary subspaces of L complementary to Δ and associate them with so-called series of type (n, s). We prove that Lagrangian subspaces are in bijection with skew-symmetric (n, s) -type series and topological quasi-Lie bialgebra structures on g [ [ x ] ] . Using the classificaiton of Manin pairs we classify up to twisting and coordinate transformations all quasi-Lie bialgebra structures. Series of type (n, s) , solving the generalized classical Yang-Baxter equation, correspond to subalgebras of L. We discuss their possible utility in the theory of integrable systems. [ABSTRACT FROM AUTHOR]

We consider three 'classical doubles' of any semisimple, connected and simply connected compact Lie group G: the cotangent bundle, the Heisenberg double and the internally fused quasi-Poisson double. On each double we identify a pair of 'master integrable systems' and investigate their Poisson reductions. In the simplest cotangent bundle case, the reduction is defined by taking quotient by the cotangent lift of the conjugation action of G on itself, and this naturally generalizes to the other two doubles. In each case, we derive explicit formulas for the reduced Poisson structure and equations of motion and find that they are associated with well known classical dynamical r-matrices. Our principal result is that we provide a unified treatment of a large family of reduced systems, which contains new models as well as examples of spin Sutherland and Ruijsenaars–Schneider models that were studied previously. We argue that on generic symplectic leaves of the Poisson quotients the reduced systems are integrable in the degenerate sense, although further work is required to prove this rigorously. [ABSTRACT FROM AUTHOR]

In order to extend the geometrization of Yangian R-matrices from Lie algebras gl (n) to superalgebras gl (M | N) , we introduce new quiver-related varieties which are associated with representations of gl (M | N) . In order to define them similarly to the Nakajima-Cherkis varieties, we reformulate the construction of the latter by replacing the Hamiltonian reduction with the intersection of generalized Lagrangian subvarieties in the cotangent bundles of Lie algebras sitting at the vertices of the quiver. The new varieties come from replacing some Lagrangian subvarieties with their Legendre transforms. We present superalgebra versions of stable envelopes for the new quiver-like varieties that generalize the cotangent bundle of a Grassmannian. We define superalgebra generalizations of the Tarasov–Varchenko weight functions, and show that they represent the super stable envelopes. Both super stable envelopes and super weight functions transform according to Yangian R ˇ -matrices of gl (M | N) with M + N = 2 . [ABSTRACT FROM AUTHOR]

We construct infinite-dimensional R-matrices that generalise the relativistic scattering of massless modes with the same chirality on AdS2 near the Berestein-Maldacena-Nastase vacuum. We show that the infrared limit of the R-matrices reproduces finite-dimensional scattering of massless modes on AdS2, from which the R-matrices borrow modified braiding unitary. We also prove that the R-matrices enjoy an infinite-dimensional symmetry superalgebra that embeds that of AdS2. Finally, we verify that the R-matrices are also invariant under crossing symmetry. [ABSTRACT FROM AUTHOR]

We construct infinite-dimensional R-matrices that generalise the relativistic scattering of massless modes with the same chirality on AdS2 near the Berestein-Maldacena-Nastase vacuum. We show that the infrared limit of the R-matrices reproduces finite-dimensional scattering of massless modes on AdS2, from which the R-matrices borrow modified braiding unitary. We also prove that the R-matrices enjoy an infinite-dimensional symmetry superalgebra that embeds that of AdS2. Finally, we verify that the R-matrices are also invariant under crossing symmetry. [ABSTRACT FROM AUTHOR]

By the supersymmetrization of a simple algebraic technique proposed in Lukierski and Tolstoy (Eur Phys J C 77:226, 2017) we obtain the complete classification of all basic (nonisomorphic) quantum deformations for the orthosymplectic Lie superalgebra osp (1 | 2 ; C) and its pseudoreal and real forms in terms of the classical r-matrices. In particular, we prove that pseudoreal compact form has only one quantum deformation (standart q-analog), and the D = 3 , N = 1 Lorentz supersymmetry, which is the non-compact real form of osp (1 | 2 ; C) , has four different Hopf-algebraic quantum deformations: two standard q-analogs, and two (Jordanian and super-Jordanian) twist deformations. All basic Hopf-algebraic quantum deformations are presented in the explicit form. [ABSTRACT FROM AUTHOR]

When the wave nature of particles plays a role in their scattering dynamics, quasi-bound states in the positive energy continuum can have a huge impact on their dynamics. This effect has been observed in nuclear scattering processes and molecular reaction dynamics. We here examine the effect of quasibound state formation in a quantum gate, and its impact on the dynamics of qudits that pass through the quantum gate. The analysis is performed using reaction matrix (R-matrix) theory, with Dirichlet boundary conditions. R-matrix theory obtains results much more efficiently than more computationally demanding methods such as mode matching techniques, tight binding Green's function methods, or finite element methods. • Electron dynamics in quantum gates affects quantum information processing networks. • Reaction matrix theory can be used to study electron dynamics in quantum gates. • R-matrix theory, applied to quantum gates, requires Dirichlet boundary conditions. • Qudit dynamics, in quantum gates, is altered significantly by resonances. • R-matrix theory is more efficient than Greens function, mode matching, or finite element methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and develop the notion of a Manin triple for a Lie superalgebra g defined over a field of characteristic p = 2. We find cohomological necessary conditions for the pair (g , g ⁎) to form a Manin triple. We introduce the concept of Lie bi-superalgebras for p = 2 and establish a link between Manin triples and Lie bi-superalgebras. In particular, we study Manin triples defined by a classical r -matrix with an extra condition (called an admissible classical r -matrix). A particular case is examined where g has an even invariant non-degenerate bilinear form. In this case, admissible r -matrices can be obtained inductively through the process of double extensions. In addition, we introduce the notion of double extensions of Manin triples, and show how to get a new Manin triple from an existing one. [ABSTRACT FROM AUTHOR]

The Multichannel Quantum Defect Theory and the Reduced R-Matrix are formally related and physically equivalent; both theories describe not only the internal dynamics but also the interactions in space of eliminated channels. One proves the Multichannel Quantum Defect Theory is Reduced Collision Matrix describing effect of eliminated channel on observed ones. The multichannel resonances originating in bound or quasistationary single particle states are described in terms of Reduced Collision Matrix. The single particle states are defined by Bound- or Quasistationary-State equation in the eliminated channel, relating channel logarithmic derivative to R-Matrix. [ABSTRACT FROM AUTHOR]

Experimental electron scattering cross sections for thiophene in the impact energy range from 1 to 300 eV have been measured with a magnetically confined electron transmission-beam apparatus. Random uncertainty limits have been estimated to be less than 5%, and systematic errors derived from acceptance angle limitations have also been identified and evaluated. Experimental values are compared with our previous low energy (1-15 eV) R-matrix and intermediate/high energy (15-300 eV) IAM-SCAR+I calculations finding reasonable agreement, within the combined uncertainty limits. Some of the low energy shape and core-excited resonances predicted by previous calculations are experimentally confirmed in this study. [ABSTRACT FROM AUTHOR]

We study the Gauge/Bethe correspondence for two-dimensional N = (2, 2) supersymmetric quiver gauge theories associated with toric Calabi-Yau three-folds, whose BPS algebras have recently been identified as the quiver Yangians. We start with the crystal representations of the quiver Yangian, which are placed at each site of the spin chain. We then construct integrable models by combining the single-site crystals into crystal chains by a coproduct of the algebra, which we determine by a combination of representation-theoretical and gauge-theoretical arguments. For non-chiral quivers, we find that the Bethe ansatz equations for the crystal chain coincide with the vacuum equation of the quiver gauge theory, thus confirming the corresponding Gauge/Bethe correspondence. For more general chiral quivers, however, we find obstructions to the R-matrices satisfying the Yang-Baxter equations and the unitarity conditions, and hence to their corresponding Gauge/Bethe correspondence. We also discuss trigonometric (quantum toroidal) versions of the quiver BPS algebras, which correspond to three-dimensional N = 2 gauge theories and arrive at similar conclusions. Our findings demonstrate that there are important subtleties in the Gauge/Bethe correspondence, often overlooked in the literature. [ABSTRACT FROM AUTHOR]

In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras, and Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative) Rota--Baxter operator on a Leibniz algebra and construct the graded Lie algebra that characterizes relative Rota--Baxter operators as Maurer--Cartan elements. By these structures and the twisting theory of twilled Leibniz algebras, we further define the classical Leibniz Yang--Baxter equation, classical Leibniz r-matrices, and triangular Leibniz bialgebras. Finally, we construct solutions of the classical Leibniz Yang--Baxter equation using relative Rota-- Baxter operators and Leibniz-dendriform algebras. [ABSTRACT FROM AUTHOR]

We consider a problem of separation of variables for Lax-integrable Hamiltonian systems governed by gl(n) ⨂ gl(n)-valued classical r-matrices r(u, v). We find a new class of classical non-skew-symmetric non-dynamical gl(n) ⨂ gl(n)-valued r-matrices rJ(u, v) for which the "magic recipe" of Sklyanin [Prog. Theor. Phys. Suppl. 118, 35 (1995)] in the theory of variable separation is applicable, i.e., for which standard separating functions A(u) and B(u) of Gekhtman [Commun. Math. Phys. 167, 593 (1995)] and Scott ["Classical functional Bethe ansatz for SL(N): Separation of variables for the magnetic chain," arXiv:hep-th 940303] produce a complete set of canonical coordinates satisfying the equations of separation. We illustrate the corresponding separation of variable theory by the example of the anisotropically deformed An Toda models proposed in the work of Skrypnyk [J. Phys. A: Math. Theor. 38, 9665–9680 (2005)] and governed by the r-matrices rJ(u, v) and by the generalized Gaudin models [T. Skrypnyk, Phys. Lett. A 334(5–6), 390 (2005)] governed by the same classical r-matrices. The n = 2 and n = 3 cases are considered in detail. [ABSTRACT FROM AUTHOR]

Interatomic Coulombic Decay (ICD) is a general mechanism in which an excited atom can transfer its excess energy to a neighbor which is thus ionized. ICD belongs to the family of Feshbach resonance processes and as such, states undergoing ICD are characterized by their energy width. In this work, we investigate the computations of ICD widths using the R-matrix method as implemented in the UKRmol package. Helium dimer is used here as a benchmark system. The results are compared with those obtained with the well established Fano-Algebraic Diagrammatic Construction method. It is shown that the R-matrix method in its present implementation provides accurate total and partial widths if the kinetic energy of the ICD electron is lower than 10 eV. Advantages and limitations of the R-matrix method on the computations of ICD widths are discussed. [ABSTRACT FROM AUTHOR]

The broadly applied notions of Lie bialgebras, Manin triples, classical r-matrices and 풪 -operators of Lie algebras owe their importance to the close relationships among them. Yet these notions and their correspondences are mostly understood as classes of objects and maps among the classes. To gain categorical insight, this paper introduces, for each of the classes, a notion of homomorphisms, uniformly called coherent homomorphisms, so that the classes of objects become categories and the maps among the classes become functors or category equivalences. For this purpose, we start with the notion of an endo Lie algebra, consisting of a Lie algebra equipped with a Lie algebra endomorphism. We then generalize the above classical notions for Lie algebras to endo Lie algebras. As a result, we obtain the notion of coherent endomorphisms for each of the classes, which then generalizes to the notion of coherent homomorphisms by a polarization process. The coherent homomorphisms are compatible with the correspondences among the various constructions, as well as with the category of pre-Lie algebras. [ABSTRACT FROM AUTHOR]

The electrons associated with molecules and other small quantum structures exist in states that are bound or quasibound to the molecule. The quasibound states, which can significantly affect chemical reaction dynamics, have finite lifetimes and are associated with complex energy poles of the scattering matrix. Using Wigner–Eisenbud (R-matrix) scattering theory, we examine the symmetry properties of the quasibound states of a molecule-size tetrahedral system, and we examine the relation of quasibound states to the scattering properties. In addition, using R-matrix theory, we construct a non-Hermitian Hamiltonian whose complex energy eigenvalues coincide with the bound and quasi-bound states of the molecule. We show that each bound state and quasibound state of the tetrahedral system belongs to a distinct irreducible representation of the tetrahedral group, and that an incident electron belonging to one irreducible representation can only scatter within the same irreducible representation. [ABSTRACT FROM AUTHOR]

For a Dynkin quiver Q (of type \mathrm {ADE}), we consider a central completion of the convolution algebra of the equivariant K-group of a certain Steinberg type graded quiver variety. We observe that it is affine quasi-hereditary and prove that its category of finite-dimensional modules is identified with a block of Hernandez-Leclerc's monoidal category \mathcal {C}_{Q} of modules over the quantum loop algebra U_{q}(L\mathfrak {g}) via Nakajima's homomorphism. As an application, we show that Kang-Kashiwara-Kim's generalized quantum affine Schur-Weyl duality functor gives an equivalence between the category of finite-dimensional modules over the quiver Hecke algebra associated with Q and Hernandez-Leclerc's category \mathcal {C}_{Q}, assuming the simpleness of some poles of normalized R-matrices for type \mathrm {E}. [ABSTRACT FROM AUTHOR]

Motivated by Maulik-Okounkov stable maps associated to quiver varieties, we define and construct algebraic stable maps on tensor products of representations in the category \mathcal {O} of the Borel subalgebra of an arbitrary untwisted quantum affine algebra. Our representation-theoretical construction is based on the study of the action of Cartan-Drinfeld subalgebras. We prove the algebraic stable maps are invertible and depend rationally on the spectral parameter. As an application, we obtain new R-matrices in the category \mathcal {O} and we establish that a large family of simple modules, including the prefundamental representations associated to Q-operators, generically commute as representations of the Cartan-Drinfeld subalgebra. We also establish categorified QQ^*-systems in terms of the R-matrices we construct. [ABSTRACT FROM AUTHOR]

Using the technique of the quasigraded Lie algebras, we construct general spectral-parameter dependent solutions r12(u, v) of the permuted classical Yang–Baxter equation with the values in the tensor square of simple Lie algebra g. We show that they are connected with infinite-dimensional Lie algebras with Adler–Kostant–Symmes decompositions and are labeled by solutions of a constant quadratic equation on the linear space g ⊕ N , N ≥ 1. We formulate the conditions when the corresponding r-matrices are skew-symmetric, i.e., they are equivalent to the ones described by Belavin–Drinfeld classification. We illustrate the developed theory by the example of the elliptic r-matrix of Sklyanin. We apply the obtained result to the explicit construction of the generalized quantum and classical Gaudin spin chains. [ABSTRACT FROM AUTHOR]

Since its initial development in the 1970s by Phil Burke and his collaborators, the R-matrix theory and associated computer codes have become the method of choice for the calculation of accurate data for general electron–atom/ion/molecule collision and photoionization processes. The use of a non-orthogonal set of orbitals based on B-splines, now called the B-spline R-matrix (BSR) approach, was pioneered by Zatsarinny. It has considerably extended the flexibility of the approach and improved particularly the treatment of complex many-electron atomic and ionic targets, for which accurate data are needed in many modelling applications for processes involving low-temperature plasmas. Both the original R-matrix approach and the BSR method have been extended to the interaction of short, intense electromagnetic (EM) radiation with atoms and molecules. Here, we provide an overview of the theoretical tools that were required to facilitate the extension of the theory to the time domain. As an example of a practical application, we show results for two-photon ionization of argon by intense short-pulse extreme ultraviolet radiation. [ABSTRACT FROM AUTHOR]

We present a simple unified formula expressing the denominators of the normalized R-matrices between the fundamental modules over the quantum loop algebras of type ADE . It has an interpretation in terms of representations of Dynkin quivers and can be proved in a unified way using geometry of the graded quiver varieties. As a by-product, we obtain a geometric interpretation of Kang–Kashiwara–Kim's generalized quantum affine Schur–Weyl duality functor when it arises from a family of the fundamental modules. We also study several cases when the graded quiver varieties are isomorphic to unions of the graded nilpotent orbits of type A . [ABSTRACT FROM AUTHOR]

Let $U_q'({\mathfrak {g}})$ be a quantum affine algebra with an indeterminate $q$ , and let $\mathscr {C}_{\mathfrak {g}}$ be the category of finite-dimensional integrable $U_q'({\mathfrak {g}})$ -modules. We write $\mathscr {C}_{\mathfrak {g}}^0$ for the monoidal subcategory of $\mathscr {C}_{\mathfrak {g}}$ introduced by Hernandez and Leclerc. In this paper, we associate a simply laced finite-type root system to each quantum affine algebra $U_q'({\mathfrak {g}})$ in a natural way and show that the block decompositions of $\mathscr {C}_{\mathfrak {g}}$ and $\mathscr {C}_{\mathfrak {g}}^0$ are parameterized by the lattices associated with the root system. We first define a certain abelian group $\mathcal {W}$ (respectively $\mathcal {W} _0$) arising from simple modules of $\mathscr {C}_{\mathfrak {g}}$ (respectively $\mathscr {C}_{\mathfrak {g}}^0$) by using the invariant $\Lambda ^\infty$ introduced in previous work by the authors. The groups $\mathcal {W}$ and $\mathcal {W} _0$ have subsets $\Delta$ and $\Delta _0$ determined by the fundamental representations in $\mathscr {C}_{\mathfrak {g}}$ and $\mathscr {C}_{\mathfrak {g}}^0$ , respectively. We prove that the pair $(\mathbb {R} \otimes _\mathbb {\mspace {1mu}Z\mspace {1mu}} \mathcal {W} _0, \Delta _0)$ is an irreducible simply laced root system of finite type and that the pair $(\mathbb {R} \otimes _\mathbb {\mspace {1mu}Z\mspace {1mu}} \mathcal {W} , \Delta)$ is isomorphic to the direct sum of infinite copies of $(\mathbb {R} \otimes _\mathbb {\mspace {1mu}Z\mspace {1mu}} \mathcal {W} _0, \Delta _0)$ as a root system. [ABSTRACT FROM AUTHOR]

The differential cross section of the deuteron elastic scattering on oxygen was studied, experimentally, in the energy range of 1.5 – 2.5 MeV, in order for the theoretical study to be accomplished in the energy range 1.9–2.5 MeV for the scattering angles of 130°, 140°, 150°, 160° and 170°.The experiment was performed at the Tandem 5.5 MV Accelerator of the N.C.S.R. "Demokritos" in Athens, Greece. The theoretical study was accomplished in order to extend the pre-existing evaluation, which stopped at 1.98 MeV, up to 2.5 MeV. The used code implements the R-matrix theory along with optical model calculations. [ABSTRACT FROM AUTHOR]

It has been a long-standing problem how to relate Chern–Simons theory to the quantum groups. In this paper we recover the classical r-matrix directly from a three-dimensional Chern–Simons theory with boundary conditions, thus creating a direct link to the quantum groups. It is known that the Jones polynomials can be constructed using an R-matrix. We show how these constructions can be seen to arise directly from 3-dimensional Chern–Simons theory. [ABSTRACT FROM AUTHOR]

k-Para-Kähler Lie algebras are a generalization of para-Kähler Lie algebras (k = 1) and constitute a subclass of k-symplectic Lie algebras. In this paper, we show that the characterization of para-Kähler Lie algebras as left symmetric bialgebras can be generalized to k-para-Kähler Lie algebras leading to the introduction of two new structures which are different but both generalize the notion of left symmetric algebra. This permits also the introduction of generalized S-matrices. We determine then all the k-symplectic Lie algebras of dimension (k + 1) and all the six dimensional 2-para-Kähler Lie algebras. [ABSTRACT FROM AUTHOR]

The elastic and excitation processes for e-N 2 H/HCO systems are investigated in this article. The calculations are performed within the framework of R-matrix theory implemented using the pseudo-state formalism. Electron attachment to N 2 H/HCO during electron collision is found to produce temporary negative ion states. We observed two negative ion states, X 1 A ′ and 3 A ′ ′ , in the elastic scattering channel for the present targets. The generation of negative ions in the inelastic (electronic excitation) channel is also observed. Formation of H - ion is traced out by investigating the dissociative electron attachment process for the e-N 2 H/HCO scattering system. A detailed investigation of the elastic and electronic excitation processes of e-N 2 H/HCO systems is reported here. The results presented here will be key to understand various intermediate processes occurring in N 2 H - and HCO-rich environments. [ABSTRACT FROM AUTHOR]