Graded decomposition numbers for cyclotomic Hecke algebras

TL;DR

This paper proves a graded version of the Lascoux-Leclerc-Thibon conjecture, providing a detailed description of decomposition numbers for graded Specht modules over cyclotomic Hecke algebras in characteristic zero.

Contribution

It introduces a graded framework for Specht modules and confirms a conjecture relating to their decomposition numbers, advancing understanding of cyclotomic Hecke algebras.

Findings

Proof of the graded Lascoux-Leclerc-Thibon conjecture

Explicit description of graded decomposition numbers

Extension of Specht module theory to graded setting

Abstract

In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic Hecke algebras. In this article, we prove a graded version of the Lascoux-Leclerc-Thibon conjecture, describing the decomposition numbers of graded Specht modules over a field of characteristic zero.