Product formula for the limits of normalized characters of Kirillov-Reshetikhin modules

TL;DR

This paper proves a conjectural product formula for the limits of normalized characters of Kirillov-Reshetikhin modules over quantum affine algebras, advancing understanding of their asymptotic behavior with some exceptions.

Contribution

It establishes the product formula for these limits, using algebraic relations akin to $Q ilde{Q}$-relations, with partial results in type $E_8$.

Findings

Confirmed the product formula for most cases.

Developed algebraic relations among limits.

Identified exceptions in type $E_8$.

Abstract

The normalized characters of Kirillov-Reshetikhin modules over a quantum affine algebra have a limit as a formal power series. Mukhin and Young found a conjectural product formula for this limit, which resembles the Weyl denominator formula. We prove this formula except for some cases in type $E_8$ by employing an algebraic relation among these limits, which is a variant of $Q\widetilde{Q}$-relations.