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Ghost center and representations of the diagonal reduction algebra of [formula omitted].
- Source :
-
Journal of Geometry & Physics . May2023, Vol. 187, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- Reduction algebras are known by many names in the literature, including step algebras, Mickelsson algebras, Zhelobenko algebras, and transvector algebras, to name a few. These algebras, realized by raising and lowering operators, allow for the calculation of Clebsch-Gordan coefficients, branching rules, and intertwining operators; and have connections to extremal equations and dynamical R-matrices in integrable face models. In this paper we continue the study of the diagonal reduction superalgebra A of the orthosymplectic Lie superalgebra osp (1 | 2). We construct a Harish-Chandra homomorphism, Verma modules, and study the Shapovalov form on each Verma module. Using these results, we prove that the ghost center (center plus anti-center) of A is generated by two central elements and one anti-central element (analogous to the Scasimir due to Leśniewski for osp (1 | 2)). As another application, we classify all finite-dimensional irreducible representations of A. Lastly, we calculate an infinite-dimensional tensor product decomposition explicitly. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*LIE superalgebras
*R-matrices
*REPRESENTATION theory
*HOMOMORPHISMS
Subjects
Details
- Language :
- English
- ISSN :
- 03930440
- Volume :
- 187
- Database :
- Academic Search Index
- Journal :
- Journal of Geometry & Physics
- Publication Type :
- Academic Journal
- Accession number :
- 162704877
- Full Text :
- https://doi.org/10.1016/j.geomphys.2023.104788