Affinizations, R-matrices and reflection functors
arXiv:2304.00238 · doi:doi.org/10.1016/j.aim.2024.109598
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.
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)