RTT realization of quantum affine superalgebras and tensor products

TL;DR

This paper explores the RTT realization of quantum affine superalgebras linked to rak{gl}(M,N), analyzing finite-dimensional representations and tensor products, with explicit cyclicity conditions for rak{gl}(1,1).

Contribution

It provides a new RTT-based framework for studying representations of quantum affine superalgebras and determines cyclicity conditions explicitly for rak{gl}(1,1).

Findings

Cyclicity conditions for tensor products in rak{gl}(1,1) are fully characterized.

Cyclicity of certain tensor products of Kirillov-Reshetikhin modules is established.

The RTT realization facilitates analysis of finite-dimensional representations.

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 $\mathfrak{gl}(M,N)$.