Weyl approach to representation theory of reflection equation algebra
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.
Keywords
Cite
@article{arxiv.math/0307024,
title = {Weyl approach to representation theory of reflection equation algebra},
author = {P. A. Saponov},
journal= {arXiv preprint arXiv:math/0307024},
year = {2009}
}
Comments
LaTeX2e file, 27 pages, no figures