Geometric Representation Theory Seminar
Monday, October 29, 2018 at 5:30pm to 6:30pm
Matt Hogancamp (USC)
The curved Hecke category and the isospectral Hilbert scheme
In this talk I will discuss a "curved" version of the Hecke category, introduced in joint work with Gorsky, whose objects can be described as certain curved complexes of Soergel bimodules. Our main result uses a certain link splitting property in the curved Hecke category to explicitly compute the Khovanov-Rozansky homologies of the (n,nk) torus links, both in the curved and uncurved settings. Summing over all k yields an explicit graded algebra considered by Haiman in his study of Hilbert schemes. Combining with an idea of Gorsky-Negut-Rasmussen, we obtain a functor from the (curved or uncurved) Hecke category to sheaves on the appropriate Hilbert scheme.