Affinizations, R-matrices and reflection functors
Representation Theory
2025-05-02 v4 Quantum Algebra
Abstract
In this paper we establish affinizations and R-matrices in the language of pro-objects, and as an application, we construct reflection functors over the localizations of quiver Hecke algebras of arbitrary finite types. This reflection functor categorifies the braid group action on the half of a quantum group and the Saito reflection.
Cite
@article{arxiv.2304.00238,
title = {Affinizations, R-matrices and reflection functors},
author = {Masaki Kashiwara and Myungho Kim and Se-jin Oh and Euiyong Park},
journal= {arXiv preprint arXiv:2304.00238},
year = {2025}
}
Comments
96 pages in v1. 79 pages, small corrections with a simplified proof of Theorem 8.3 in v2. In v3, Sections 9.3 and 11 are added. In v4, we added Lemma 6.16 and Lemma 8.8, and made numerous minor changes (104 pages)