Graded decomposition matrices of v-Schur algebras via Jantzen filtration

TL;DR

This paper proves that specific parabolic Kazhdan-Lusztig polynomials determine the graded decomposition matrices of v-Schur algebras through the Jantzen filtration, confirming a conjecture by Leclerc and Thibon.

Contribution

It establishes a direct link between Kazhdan-Lusztig polynomials and the graded decomposition matrices of v-Schur algebras, confirming a key conjecture.

Findings

Kazhdan-Lusztig polynomials compute graded decomposition matrices

Confirmation of Leclerc and Thibon's conjecture

Advancement in understanding v-Schur algebra representations

Abstract

We prove that certain parabolic Kazhdan-Lusztig polynomials calculate the graded decomposition matrices of v-Schur algebras given by the Jantzen filtration of Weyl modules, confirming a conjecture of Leclerc and Thibon.