English

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 GL2\mathrm{GL}_2, 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

R2 v1 2026-06-23T07:55:45.109Z