A cluster algebra approach to q-characters of Kirillov-Reshetikhin modules

TL;DR

This paper introduces a cluster algebra-based algorithm to compute q-characters of Kirillov-Reshetikhin modules in quantum affine algebras, extending geometric formulas and connecting to quiver variety homology.

Contribution

It presents a novel cluster algebra approach for q-character calculations applicable to all untwisted quantum affine algebras, generalizing existing geometric formulas.

Findings

Provides a universal algorithm for q-characters of Kirillov-Reshetikhin modules.

Extends Nakajima's geometric formula to broader cases.

Establishes a link between cluster algebras and quantum affine algebra representations.

Abstract

We describe a cluster algebra algorithm for calculating q-characters of Kirillov-Reshetikhin modules for any untwisted quantum affine algebra. This yields a geometric q-character formula for tensor products of Kirillov-Reshetikhin modules. In simply laced type this formula extends Nakajima's formula for q-characters of standard modules in terms of homology of graded quiver varieties.