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28 March 2024
 
  » arxiv » math.QA/0307024

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Weyl approach to representation theory of reflection equation algebra
P. A. Saponov ;
Date 2 Jul 2003
Subject Quantum Algebra; Representation Theory | math.QA math.RT
AbstractThe present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum groups). We suggest a universal method of constructing finite dimensional irreducible non-commutative 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 which 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 the direct sum of irreducible components is also suggested.
Source arXiv, math.QA/0307024
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