Cluster algebras and quantum affine algebras

TL;DR

This paper explores the structure of finite-dimensional representations of quantum affine algebras of simply-laced type by introducing monoidal subcategories and analyzing their Grothendieck rings through the lens of cluster algebras.

Contribution

It introduces monoidal subcategories of the representation category and applies cluster algebra techniques to study their Grothendieck rings.

Findings

Defined monoidal subcategories C_l of the representation category

Connected Grothendieck rings of these subcategories to cluster algebras

Provided new insights into the algebraic structure of quantum affine algebra representations

Abstract

Let C be the category of finite-dimensional representations of a quantum affine algebra of simply-laced type. We introduce certain monoidal subcategories C_l (l integer) of C and we study their Grothendieck rings using cluster algebras.