It is well known that Hecke algebra is spanned by braids modulo skein relations, while the span of closed braids in the annulus modulo skein relations is isomorphic to the space of symmetric functions. I will describe a categorification of these results: the category of Soergel bimodules categorifies the Hecke algebra, while the annular closure corresponds to the formalism of “derived horizontal trace”. Along the way, I will explicitly compute Hochschild homology of the category of Soergel bimodules.
All notions will be explained in the talk. This is a joint work with Matt Hogancamp and Paul Wedrich.
This is a part of the "GRT at home" seminar series, see grt-home.org
Note the unusual time!