PreprintRepresentations of twisted qYangiansLucy Gow and Alexander MolevAbstractThe twisted qYangians are coideal subalgebras of the quantum affine algebra associated with gl(N). We prove a classification theorem for finitedimensional irreducible representations of the twisted qYangians associated with the symplectic Lie algebras sp(2n). The representations are parameterized by their highest weights or by their Drinfeld polynomials. In the simplest case of sp(2) we give an explicit description of all the representations as tensor products of evaluation modules. We prove analogues of the PoincareBirkhoffWitt theorem for the quantum affine algebra and for the twisted qYangians. We also reproduce a proof of the classification theorem for finitedimensional irreducible representations of the quantum affine algebra by relying on its Rmatrix presentation. This paper is available as a pdf (385kB) file.
