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Weyl approach to representation theory of reflection equation algebra

P. A. Saponov
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Abstract

The 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.

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P. A. Saponov. 2003-07-02. Weyl approach to representation theory of reflection equation algebra. https://doi.org/10.1088/0305-4470/37/18/008

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