The Lascoux, Leclerc and Thibon algorithm and Soergel's tilting algorithm

TL;DR

This paper extends Soergel's tilting algorithm to singular weights and confirms the Lascoux-Leclerc-Thibon conjecture, linking canonical bases in Fock modules to Hecke algebra representations at roots of unity.

Contribution

It generalizes Soergel's tilting algorithm to singular weights and proves the Lascoux-Leclerc-Thibon conjecture.

Findings

Validation of the Lascoux-Leclerc-Thibon conjecture

Extension of tilting algorithm to singular weights

Connection established between canonical bases and Hecke algebra representations

Abstract

We generalize Soergel's tilting algorithm to singular weights and deduce from this the validity of the Lascoux-Leclerc-Thibon conjecture on the connection between the canonical basis of the basic submodule of the Fock module and the representation theory of the Hecke-algebras at root of unity.