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

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.

arXiv comment17 pages; minor edits to address referee's comments; final version

References in corpus (8)

• Diagrammatics for Soergel categories
• The two-color Soergel calculus
• Homology of torus knots
• Hilbert schemes and $y$-ification of Khovanov-Rozansky homology
• Free-monodromic mixed tilting sheaves on flag varieties
• Khovanov-Rozansky homology and higher Catalan sequences
• Idempotents in triangulated monoidal categories
• Torus link homology