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.

arXiv commentLaTeX2e file, 27 pages, no figures

References in corpus (8)

• Algebraic Structures Related to Reflection Equations
• Differential Geometry on Linear Quantum Groups
• Constant Solutions of Reflection Equations and Quantum Groups
• GLq(N)-Covariant Quantum Algebras and Covariant Differential Calculus
• On universal solution to reflection equation
• Quantum line bundles on noncommutative sphere
• Traces in braided categories
• Extended reflection equation algebras, the braid group on a handlebody and associated link polynomials

Cited by in corpus (3)

• Braided Differential Operators on Quantum Algebras
• Asymmetric Twin Representation: the Transfer Matrix Symmetry
• q-Casimir and q-cut-and-join operators related to Reflection Equation Algebras