Representations of quantum affine algebras of type B_{N}

Abstract

We study finite-dimensional representations of quantum affine algebras of type $ B_N$. We show that a module is tame if and only if it is thin. In other words, the Cartan currents are diagonalizable if and only if all joint generalized eigenspaces have dimension one. We classify all such modules and describe their $ q$-characters. In some cases, the $ q$-characters are described by super standard Young tableaux of type $ (2N\vert 1)$.