Categorification of a recursive formula for Kazhdan-Lusztig polynomials

TL;DR

This paper develops a categorification of a recursive formula for Kazhdan-Lusztig polynomials by deriving explicit branching rules for modules over certain bimodule endomorphism algebras.

Contribution

It introduces explicit branching rules for modules that enable the categorification of a recursive Kazhdan-Lusztig polynomial formula.

Findings

Explicit branching rules for graded modules

Categorification of the recursive Kazhdan-Lusztig formula

Enhanced understanding of module structures in representation theory

Abstract

We obtain explicit branching rules for graded cell modules and graded simple modules over the endomorphism algebra of a Bott-Samelson bimodule. These rules allow us to categorify a well-known recursive formula for Kazhdan-Lusztig polynomials.