RTT Realization of Quantum Affine Superalgebras and Tensor Products

Abstract

We use the RTT realization of the quantum affine superalgebra associated with the Lie superalgebra |$\mathfrak {gl}(M,N)$| to study its finite-dimensional representations and their tensor products. In the case |$\mathfrak {gl}(1,1)$|⁠, the cyclicity condition of tensor products of finite-dimensional simple modules is determined completely in terms of zeros and poles of rational functions. This in turn induces cyclicity of some particular tensor products of Kirillov–Reshetikhin modules related to |$\mathfrak {gl}(M,N)$|⁠.