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arXiv · 1903.00461

Ext-enhanced monoidal Koszul duality for $\mathrm{GL}_2$

Matthew Hogancamp·Shotaro Makisumi
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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 $\mathrm{GL}_2$, working in the language of the second-named author's joint work with Achar, Riche, and Williamson.

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BibTeXRIS

Matthew Hogancamp, Shotaro Makisumi. 2019-03-01. Ext-enhanced monoidal Koszul duality for $\mathrm{GL}_2$. https://arxiv.org/abs/1903.00461

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