Representations of twisted q-Yangians

摘要: The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with \({\mathfrak{gl}_N}\) . We prove a classification theorem for finite-dimensional irreducible representations symplectic Lie algebras \({\mathfrak{sp}_{2n}}\) parameterized by their highest weights satisfying certain dominance-type conditions. In simplest case \({\mathfrak{sp}_2}\) , we give an explicit description all as tensor products evaluation modules. new proofs (well-known) Poincare–Birkhoff–Witt and in RTT-presentations. also reproduce Tarasov’s proof relying on its R-matrix presentation.