Character Formulas for Kirillov-Reshetikhin Modules via Folding of Supercharacters of $\mathfrak{gl}(M|N)$

TL;DR

This paper develops explicit character formulas for Kirillov-Reshetikhin modules of quantum affine algebras by folding supercharacters of rak{gl}(M|N), confirming a conjecture from Bethe ansatz analysis.

Contribution

It introduces a folding procedure for supercharacters of rak{gl}(M|N) to derive formulas for quantum affine modules, linking superalgebra characters with quantum affine representations.

Findings

Derived decomposition formulas for supercharacters.

Provided explicit character formulas for Kirillov-Reshetikhin modules.

Confirmed a conjecture from Bethe ansatz analysis.

Abstract

We derive decomposition formulas for supercharacters of quantum affine ortho-symplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type identities for supersymmetric Schur functions. These formulas are obtained via a folding (reduction) procedure applied to the supercharacters of the finite-dimensional general linear Lie superalgebra $\mathfrak{gl}(M|N)$. As a special case, our results provide explicit character formulas for a class of Kirillov--Reshetikhin modules of quantum affine algebras (and their Yangian counterparts), thereby proving a previously proposed conjecture derived from Bethe ansatz analysis (arXiv:2309.16660).