A comparison of q-decomposition numbers in the q-deformed Fock spaces of higher levels.

link: http://arxiv.org/abs/1102.1780
Abstract

The $q$-deformed Fock spaces of higher levels were introduced by
Jimbo-Misra-Miwa-Okado. The $q$-decomposition matrix is a transition matrix
from the standard basis to the canonical basis defined by Uglov in the
$q$-deformed Fock space. In this paper, we show that parts of $q$-decomposition
matrices of level $\ell$ coincides with that of level $\ell - 1$ under certain
conditions of multi charge.