Monodromic model for Khovanov-Rozansky homology
Abstract
We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify the objects representing individual Hochschild cohomology groups (for the zero and the top degree cohomology this reduces to an earlier result of Gorsky, Hogancamp, Mellit and Nakagane). These objects turn out to be closely related to explicit character sheaves corresponding to exterior powers of the reflection representation of the Weyl group. Applying the described functors to the images of braids in the Hecke category of type A we obtain a geometric description for Khovanov-Rozansky knot homology, essentially different from the one considered earlier by Webster and Williamson.
Keywords
Cite
@article{arxiv.2008.11379,
title = {Monodromic model for Khovanov-Rozansky homology},
author = {Roman Bezrukavnikov and Kostiantyn Tolmachov},
journal= {arXiv preprint arXiv:2008.11379},
year = {2022}
}
Comments
57 pages, major revision. One of the main results (now Theorem 5.6.1), previously proved for type A only, was generalized to arbitrary type. Results specific to type A reorganized to a new Section 6