Kazhdan-Lusztig combinatorics in the moment graph setting

TL;DR

This paper extends equalities related to Kazhdan-Lusztig polynomials to the moment graph setting, providing proofs valid in positive characteristic under certain conditions, with implications for the graded ranks of sheaf stalks.

Contribution

It introduces a novel approach to Kazhdan-Lusztig combinatorics within the moment graph framework, applicable in positive characteristic contexts.

Findings

Lifted equalities to the moment graph setting

Proofs valid in positive characteristic under assumptions

Connections to graded ranks of sheaf stalks

Abstract

Motivated by a question on the graded rank of the stalks of the canonical sheaf on a Bruhat graph, we lift some equalities concerning (parabolic) Kazhdan-Lusztig polynomials to this moment graph setting. Our proofs hold also in positive characteristic, under some technical assumptions.