FINITE-DIMENSIONAL IRREDUCIBLE REPRESENTATIONS OF REFLECTION ALGEBRA FOR SU(1,1)(Q) VERTEX MODEL - CLASSIFICATION, BOSON-FERMION REALIZATIONS, AND YANG-BAXTERIZATION

Finite-dimensional irreducible representations of a reflection algebra related to the reflection equation for the su(1,1)q model are classified. It is proven that this algebra has two inequivalent one-dimensional and one two-dimensional irreducible representations. Some indecomposable representations are also constructed and the (q-boson-)fermion realizations are explicitly presented. Finally, the Yang-Baxterization of this algebra and its constant solutions (the one-dimensional representations) is investigated.