Fundamental representations of quantum affine superalgebras and R-matrices

TL;DR

This paper investigates fundamental representations of quantum affine superalgebras related to general linear Lie superalgebras, computing R-matrix denominators and establishing conditions for tensor product simplicity.

Contribution

It introduces explicit calculations of R-matrix denominators and provides criteria for the cyclicity and simplicity of tensor products of fundamental representations.

Findings

Computed denominators of rational R-matrices between fundamental representations

Proved cyclicity condition for tensor products of fundamental representations

Established simplicity criteria for tensor products

Abstract

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices between two fundamental representations are computed; a cyclicity (and so simplicity) condition on tensor products of fundamental representations is proved.