6 papers · 1 filter
Calculating double-leaf coefficients in the Hecke category
Colton Sandvik
Given a morphism of Abe-Bott-Samelson bimodules, we construct an algorithm for computing its double-leaves coefficients. The key ingredient is a modification of Bruhat upper-triang…
Soergel calculus for monodromic Hecke categories
Colton Sandvik
We introduce two 2-categories which categorify the monodromic Hecke algebra. The first is algebraic in nature and generalizes Abe's theory of Soergel bimodules. The second is a dia…
Relative Serre duality for Coxeter groups
Colton Sandvik
It was conjectured by Gorsky, Hogancamp, Mellit, and Nakagane that the left and right adjoints of the parabolic induction functor between homotopy categories of Soergel bimodules a…
A Betti geometric Casselman-Shalika equivalence
Colton Sandvik
Whittaker sheaves are ubiquitous in geometric representation theory; however, their definition requires one to restrict the sheaf-theoretic setting to either étale sheaves or -m…
Endoscopy for Modular Hecke Categories
Colton Sandvik
Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this forma…
Modular Character Sheaves on Reductive Lie Algebras
Colton Sandvik
Mirković introduced the notion of character sheaves on a Lie algebra. Due to their simple geometric characterization, character sheaves on Lie algebras can be thought of as a simpl…