A diagrammatic approach to reflection functors
Representation Theory
2025-12-23 v3
Abstract
We construct reflection functors for quiver Hecke algebras associated with arbitrary symmetrizable Kac-Moody algebras, from a higher representation-theoretic viewpoint. These functors provide a categorification of Lusztig's braid group action on the quantum group. Similar functors were recently constructed independently by Kashiwara-Kim-Oh-Park via a different approach. Moreover, we prove that our reflection functors satisfy the braid relations as natural isomorphisms.
Cite
@article{arxiv.2506.17070,
title = {A diagrammatic approach to reflection functors},
author = {Haruto Murata},
journal= {arXiv preprint arXiv:2506.17070},
year = {2025}
}
Comments
v3: 147 pages, added references, minor corrections