Representation theory of the reflection equation algebra III: Classification of irreducible representations

We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the $R$-matrix associated to the $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We develop a form of highest weight theory and use it to classify the irreducible bounded $\ast$-representations of the reflection equation algebra.