Year: 2025
Type: article
Abstract: For the group $\textrm{GL}_{n}$, we construct an action of the equivariant derived category of coherent sheaves on the Grothendieck–Springer resolution on a certain subcategory of a finite monodromic Hecke category. We use this to construct a partial categorification of the projection from the extended affine to the finite Hecke algebra of $\textrm{GL}_{n}$. As a crucial intermediate step, we compute the exterior powers, with respect to the perversely truncated multiplicative convolution, of a parabolic Springer sheaf corresponding to a maximal parabolic subgroup fixing a line in the defining $n$-dimensional representation of $\textrm{GL}_{n}$.
DOI: 10.1093/imrn/rnaf324
Author: Kostiantyn Tolmachov
Institution: Universität Hamburg
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415521148