Monodromic model for Khovanov–Rozansky homology

Abstract We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on monodromic Hecke category studied earlier by first author and Yun. Moreover, we identify objects representing individual groups (for zero top degree this reduces to an result Gorsky, Hogancamp, Mellit Nakagane). These turn out be closely related explicit character sheaves corresponding exterior powers reflection representation Weyl group. Applying described functors images braids in type A obtain description Khovanov–Rozansky knot homology, essentially different from one considered Webster Williamson.