Representations of twisted q-Yangians

The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with gl(N). We prove a classification theorem for finite-dimensional irreducible representations of the twisted q-Yangians associated with the symplectic Lie algebras sp(2n). The representations are parameterized by their highest weights satisfying certain dominance-type conditions. In the simplest case of sp(2), we give an explicit description of all the representations as tensor products of evaluation modules. We give new proofs of the (well-known) Poincare-Birkhoff-Witt theorem for the quantum affine algebra and for the twisted q-Yangians in their RT T-presentations. We also reproduce Tarasov's proof of the classification theorem for finite-dimensional irreducible representations of the quantum affine algebra by relying on its R-matrix presentation.