# Quantum affine algebras and cluster algebras

## TL;DR

This paper explores the relationship between quantum affine algebras and cluster algebras, focusing on their monoidal categories and the structure of their Grothendieck rings, based on a minicourse from a 2018 summer school.

## Contribution

It presents new results and conjectures on the structure of monoidal categories of quantum affine algebra representations and their connection to cluster algebras.

## Key findings

- Grothendieck rings of quantum affine algebra representations have cluster algebra structures
- Identification of monoidal categories with cluster algebra frameworks
- Formulation of conjectures relating quantum affine algebras and cluster algebras

## Abstract

This article is an extended version of the minicourse given by the second author at the summer school of the conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification", held in June 2018 in Washington. The aim of the minicourse, consisting of three lectures, was to present a number of results and conjectures on certain monoidal categories of finite-dimensional representations of quantum affine algebras, obtained by exploiting the fact that their Grothendieck rings have the natural structure of a cluster algebra.