7 papers
Gluing parabolic character sheaves
Kostiantyn Tolmachov
We introduce and study the category of unipotent character sheaves on the non-degenerate locus of the Vinberg semigroup associated to a reductive group of adjoint type. We show tha…
Generalized Markov traces and Jucys-Murphy elements
Kostiantyn Tolmachov, Heorhii Zhylinskyi
We give a simple construction of Markov traces for Iwahori-Hecke algebras associated with infinite series of crystallographic Coxeter groups. In types B and D it is new, and genera…
On a t-exactness property of the Harish-Chandra transform
Roman Gonin, Andrei Ionov, Kostiantyn Tolmachov
Using hyperbolic localization, we identify the nearby cycles along the Vinberg degeneration with the composition of Radon and Harish-Chandra functors, both considered for the categ…
Linear structure on a finite Hecke category in type A
Kostiantyn Tolmachov
For the group GL(n), we construct an action of the equivariant derived category of coherent sheaves on the Grothendieck-Springer resolution on a certain subcategory of a finite mon…
Equivariant derived category of a reductive group as a categorical center
Roman Bezrukavnikov, Andrei Ionov, Kostiantyn Tolmachov +1
We prove that the adjoint equivariant derived category of a reductive group is equivalent to the appropriately defined monoidal center of the torus-equivariant version of the H…
Exterior powers of a parabolic Springer sheaf on a Lie algebra
Roman Bezrukavnikov, Kostiantyn Tolmachov
We compute the exterior powers, with respect to the additive convolution on the general linear Lie algebra, of a parabolic Springer sheaf corresponding to a maximal parabolic subgr…
Monodromic model for Khovanov-Rozansky homology
Roman Bezrukavnikov, Kostiantyn Tolmachov
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, w…