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 $s_k=\operatorname{Tr}_qL^k$ 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.