Ext-enhanced monoidal Koszul duality for $\mathrm{GL}_2$
Representation Theory
2020-03-23 v2
Abstract
The Hecke category participates in an equivalence called monoidal Koszul duality, which exchanges it with the category of (Langlands-dual) "free-monodromic tilting sheaves." Motivated by a recent conjecture of Gorsky and the first-named author on HOMFLYPT link homology, we propose to enhance this duality with an additional grading. We provide evidence for this enhancement in the case of , working in the language of the second-named author's joint work with Achar, Riche, and Williamson.
Keywords
Cite
@article{arxiv.1903.00461,
title = {Ext-enhanced monoidal Koszul duality for $\mathrm{GL}_2$},
author = {Matthew Hogancamp and Shotaro Makisumi},
journal= {arXiv preprint arXiv:1903.00461},
year = {2020}
}
Comments
17 pages; minor edits to address referee's comments; final version