The anti-spherical Hecke categories for Hermitian symmetric pairs

TL;DR

This paper computes p-Kazhdan--Lusztig polynomials for Hermitian symmetric pairs and establishes the standard Koszul property of associated anti-spherical Hecke categories, advancing understanding of their algebraic structure.

Contribution

It introduces the calculation of p-Kazhdan--Lusztig polynomials and proves the standard Koszul property for anti-spherical Hecke categories in Hermitian symmetric pairs.

Findings

Computed p-Kazhdan--Lusztig polynomials for Hermitian symmetric pairs

Proved anti-spherical Hecke categories are standard Koszul

Lifted the combinatorial invariance conjecture to graded Morita equivalences

Abstract

We calculate the $p$-Kazhdan--Lusztig polynomials for Hermitian symmetric pairs and prove that the corresponding anti-spherical Hecke categories categories are standard Koszul. We prove that the combinatorial invariance conjecture can be lifted to the level of graded Morita equivalences between subquotients of these Hecke categories.