Localization for quiver Hecke algebras

Date
2019/01/31 Thu 10:30 - 12:00
Speaker
Euiyong Park
Affiliation
University of Seoul
Abstract

In this talk, I explain my recent work with Masaki Kashiwara, Myungho Kim and Se-jin Oh on a generalization of the localization procedure for monoidal categories developed in [S.-J. Kang, M. Kashiwara and M. Kim, Symmetric quiver Hecke algebras and R-matrices of
quantum affine algebras, Invent. Math. 211 (2018), no. 2, 591–685]. Let $R$ be a quiver Hecke algebra of arbitrary symmetrizable type and $R$-gmod the category of finite-dimensional graded $R$-modules. For an element w of the Weyl group, $C_w$ is the subcategory of $R$-gmod which categorifies the quantum unipotent coordinate algebra $A_q(n(w))$. We introduce the notions of braiders and a real commuting family of braiders, and produce a localization procedure which is applicable more general cases. We then construct the localization $\tilde{C}_w$ of $C_w$ by adding the inverses of simple modules which correspond to the frozen variables in the quantum cluster algebra $A_q(n(w))$. The localization $\tilde{C}_w$ is left rigid and it is conjectured that $\tilde{C}_w$ is rigid.

This seminar is hold at RIMS room 006