  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.

Representation Theory