Monoidal categorification and quantum affine algebras II
Abstract
We introduce a new family of real simple modules over the quantum affine algebras, called the affine determinantial modules, which contains the Kirillov-Reshetikhin (KR)-modules as a special subfamily, and then prove T-systems among them which generalize the T-systems among KR-modules and unipotent quantum minors in the quantum unipotent coordinate algebras simultaneously. We develop new combinatorial tools: admissible chains of i-boxes which produce commuting families of affine determinantial modules, and box moves which describe the T-system in a combinatorial way. Using these results, we prove that various module categories over the quantum affine algebras provide monoidal categorifications of cluster algebras. As special cases, Hernandez-Leclerc categories provide monoidal categorifications of the cluster algebras for an arbitrary quantum affine algebra.
Cite
@article{arxiv.2103.10067,
title = {Monoidal categorification and quantum affine algebras II},
author = {Masaki Kashiwara and Myungho Kim and Se-jin Oh and Euiyong Park},
journal= {arXiv preprint arXiv:2103.10067},
year = {2022}
}
Comments
This paper is the complete version of the announcement arXiv:2005.10969v1. 77 pages. v3 replaces the wrong version 2, 95 pages