Factorization of the canonical bases for higher level Fock spaces

TL;DR

This paper proves that the transition matrices between two canonical bases in higher level Fock spaces are unitriangular with polynomial coefficients, providing a quantum version of a decomposition matrix factorization theorem related to Ariki-Koike algebras.

Contribution

It establishes the unitriangularity of transition matrices between bases in higher level Fock spaces, linking to a quantum factorization of decomposition matrices.

Findings

Transition matrices are unitriangular with coefficients in N[v]

Provides a quantum analogue of a theorem by Geck and Rouquier

Connects Fock space bases to decomposition matrices of Ariki-Koike algebras

Abstract

The level l Fock space admits canonical bases G_e and G_\infty. They correspond to U_{v}(hat{sl}_{e}) and U_{v}(sl_{\infty})-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in N[v]. Restriction to the highest weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki-Koike algebras.