Higher-Dimensional Representations of the Reflection Equation Algebra

We consider a new method for constructing finite-dimensional irreducible representations of the reflection equation algebra. We construct a series of irreducible representations parameterized by Young diagrams. We calculate the spectra of central elements sk = TrqLk of the reflection equation algebra on “q-symmetric” and “q-antisymmetric” representations. We propose a rule for decomposing the tensor product of representations into irreducible representations.