# Quantum periodicity and Kirillov-Reshetikhin modules

## TL;DR

This paper proves the periodicity of quantum T-systems of type A with specific boundary conditions, using categorification and representation theory of quantum affine algebras, focusing on Kirillov-Reshetikhin modules.

## Contribution

It provides a new proof of quantum T-system periodicity based on categorification and representation theory, linking modules and evaluation modules.

## Key findings

- Established periodicity of quantum T-systems of type A
- Connected T-system relations with Kirillov-Reshetikhin modules
- Used categorification to relate algebraic structures

## Abstract

We give a proof of the periodicity of quantum $T$-systems of type $A_n\times A_\ell$ with certain spiral boundary conditions. Our proof is based on categorification of the $T$-system in terms of the representation theory of quantum affine algebras, more precisely on relations between classes of Kirillov-Reshetikhin modules and of evaluation modules.