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In this paper, we have considered the q deformation of the AKNS-D hierarchy, proved the bilinear identity and obtained the τ function of the q deformed AKNS-D hierarchy.

A quantum dynamical $\check{R}$-matrix with spectral parameter is constructed by fusion procedure. This spin-1 $\check{R}$-matrix is connected with Lie algebra $so(3)$ and does not satisfy the condition of translation invariance.

We obtain Drinfel'd's realization of quantum affine superalgebra $U_q\hat{(gl(1|1))}$ based on the super version of RS construction method and Gauss decomposition.

On the basis of graded RTT formalism,the defining relation of the super-Yangian Y(gl(1|1)) is derived and its oscillator realization is constructed., 7 pages, latex, no figures, to appaer in the International Workshop on Frontiers in Quantum Field Theory,Urumqi,11-18,Augast,1996

In this paper all eight-vertex type solutions of the coloured Yang - Baxter equation dependent on spectral as well as colour parameters are given. It is proved that they are composed of three groups of basic solutions, three groups of their degenerate forms and two groups of trivial solutions up to five solution transformations. Moreover, all non-trivial solutions can be classified into two types called Baxter type and free-fermion type.

In this paper, symmetries and spectral‐dependent six‐vertex‐type solutions of the colored Yang–Baxter equation are discussed. It is shown that each nondegenerate six‐vertex‐type solution of the colored Yang–Baxter equation is equivalent to one of the six basic solutions up to five solution transformations and all solutions can be classified into two types called the Baxter type and the free‐Fermion type.

The authors prove that the differential calculi on quantum groups of A-series given in this letter and in previous papers are *-calculi.

It is shown that the Beltrami equation has an infinite‐dimensional symmetry, namely the Beltrami algebra, on its solution spaces. The Beltrami algebra with central extension and its supersymmetric version are explicitly found.

The symmetries, especially those related to the $R$-transformation, of the reflection equation(RE) for two-component systems are analyzed. The classification of solutions to the RE for eight-, six- and seven-vertex type $R$-matrices is given. All solutions can be obtained from those corresponding to the standard $R$-matrices by $K$-transformation. For the free-Fermion models, the boundary matrices have property $tr K_+(0)=0$, and the free-Fermion type $R$-matrix with the same symmetry as that of Baxter type corresponds to the same form of $K_-$-matrix for the Baxter type. We present the Hamiltonians for the open spin systems connected with our solutions. In particular, the boundary Hamiltonian of seven-vertex models was obtained with a generalization to the Sklyanin's formalism., Comment: LaTeX, 16 pages

We extend the study on the algebraic structure of the $su(n)$ color Calogero-Sutherland models to the case of $gl(n|m)$ color CS model and show that the generators of the super-Yangian $Y(gl(n|m))$ can be obtained from two $gl(n|m)$ loop algebras. Also, a super $W_{\infty}$ algebra for the SUSY CS model is constructed., LaTeX, 13 pages

We extend Yangian double to super (or graded) case and give its Drinfel'd generators realization by Gauss decomposition., Comment: 6 pages, Latex, no figures

We investigate the superprincipal bundle and its associated superbundle. The super(nonlinear)connection on the superfiber bundle is constructed. Then by means of the connection theory, we establish the fermionic covariant prolongation structure theory of the supernonlinear evolution equation. In this geometry theory, the fermionic covariant fundamental equations determining the prolongation structure are presented. As an example, the supernonlinear Schrodinger equation is analyzed in the framework of this fermionic covariant prolongation structure theory. We obtain its Lax pairs and Backlund transformation.

The Heisenberg supermagnet model is an integrable supersymmetric system and has a close relationship with the strong electron correlated Hubbard model. In this paper, we investigate the integrable higher order deformations of Heisenberg supermagnet models with two different constraints: (i) S2=3S−2I for S∊USPL(2/1)/S(U(2)×U(1)) and (ii) S2=S for S∊USPL(2/1)/S(L(1/1)×U(1)). In terms of the gauge transformation, their corresponding gauge equivalent counterparts are derived.