Representations of twisted q-Yangians

The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with glN. We prove a classification theorem for finite-dimensional irreducible representations of the twisted q-Yangians associated with the symplectic Lie algebras sp2n. The representations are parameterized by their highest weights or by their Drinfeld polynomials. In the simplest case of sp2 we give an explicit description of all the representations as tensor products of evaluation modules. We prove analogues of the Poincaré–Birkhoff–Witt theorem for the quantum affine algebra and for the twisted q-Yangians. We also reproduce a proof of the classification theorem for finite-dimensional irreducible representations of the quantum affine algebra by relying on its R-matrix presentation