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 s _k=Tr_q L ^k 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.