On the theory of $q$-characters for quantum affine superalgebras of type $A$

TL;DR

This paper develops the theory of $q$-characters for quantum affine superalgebras of type $A$, connecting it with deformed Cartan matrices and providing computational tools for finite-dimensional modules.

Contribution

It introduces a multiplicative formula for the universal $R$-matrix and proposes an algorithm for computing $q$-characters of simple modules.

Findings

Derived a 2-parameter deformation of Cartan matrices for super type $A$

Established a multiplicative formula for the universal $R$-matrix

Proposed a Frenkel-Mukhin-type algorithm for $q$-characters

Abstract

We develop the theory of $q$-characters for quantum affine superalgebras of type $A$ in connection with deformed Cartan matrices. To achieve this, we establish a Khoroshkin-Tolstoy-type multiplicative formula of the universal $R$-matrix of the associated generalized quantum group, from which one can read off a 2-parameter deformation of Cartan matrices of super type $A$. We also propose a Frenkel-Mukhin-type algorithm for $q$-characters of finite-dimensional simple modules with integral highest $\ell$-weights.