2003/07/02 by Pavel Saponov, P. A. Saponov · 12 citations
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Fundamental representation #Geometry #Irreducible representation #Lie algebra #Mathematics #Matrix (chemical analysis) #Molecular spectroscopy and chirality #Product (mathematics) #Pure mathematics #Reflection (computer programming) #Representation (politics) #Representation theory #Representation theory of SU #Representation theory of finite groups #Spectrum (functional analysis) #Tensor (intrinsic definition) #Tensor product #Weight #Weyl group #math.QA #math.RT
paper · pdf · doi:10.1088/0305-4470/37/18/008
published in Journal of Physics A Mathematical and General 37(18), 5021-5046 (Institute of Physics) · LaTeX2e file, 27 pages, no figures
arxiv created 2003/07/02 · openalex publication_date 2004/04/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The present paper deals with the representation theory of reflection equation algebra, connected to a Hecke type R -matrix. Up to some reasonable additional conditions, the R -matrix is arbitrary (not necessary originating from quantum groups). We suggest a universal method for constructing finite dimensional irreducible representations in the framework of the Weyl approach well known in the representation theory of classical Lie groups and algebras. With this method a series of irreducible modules is constructed. The modules are parametrized by Young diagrams. The spectrum of central elements s k = Tr q L k is calculated in the single-row and single-column representations. A rule for the decomposition of the tensor product of modules into a direct sum of irreducible components is also suggested.