2014/05/31 by Takuya Matsumoto, Alexander Molev · 12 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Class (philosophy) #Degenerate energy levels #Homotopy and Cohomology in Algebraic Topology #Irreducible element #Irreducible representation #Lie superalgebra #Representation theory of SU #Superalgebra #Supermatrix #math-ph #math.MP #math.RT
paper · pdf · doi:10.1063/1.4896396
published in Journal of Mathematical Physics 55(9) (American Institute of Physics) · 27 pages, references added
openalex publication_date 2014/09/01 · arxiv created 2014/09/15 · arxiv updated 2015/03/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The symmetries provided by representations of the centrally extended Lie superalgebra \documentclass[12pt]minimal\begindocument\mathfrak psl(2|2)\enddocumentpsl(2|2) are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory correspondence and one-dimensional Hubbard model. We give a complete description of finite-dimensional irreducible representations of this superalgebra thus extending the work of Beisert which deals with a generic family of representations. Our description includes a new class of modules with degenerate eigenvalues of the central elements. Moreover, we construct explicit bases in all irreducible representations by applying the techniques of Mickelsson–Zhelobenko algebras.