Representations of quantum affine superalgebras

Abstract

We study the quantum affine superalgebra Uq(Lsl(M,N)) and its finite-dimensional representations. We prove a triangular decomposition and establish a system of Poincaré-Birkhoff-Witt generators for this superalgebra, both in terms of Drinfel’d currents. We define the Weyl modules in the spirit of Chari–Pressley and prove that these Weyl modules are always finite-dimensional and non-zero. In consequence, we obtain a highest weight classification of finite-dimensional simple representations when M≠N. Some concrete simple representations are constructed via evaluation morphisms.