Beyond Rouquier partitions

Abstract

We obtain closed formulas, in terms of Littlewood-Richardson coefficients, for the canonical basis elements of the Fock space representation of Uv (over(sl, ̂)e) which are labeled by partitions having 'locally small' e-quotients and arbitrary e-cores. We further show that upon evaluation at v = 1, this gives the corresponding decomposition numbers of the q-Schur algebra in characteristic l (where q is a primitive eth root of unity if l ≠ e and q = 1 otherwise) whenever l is greater than the size of each constituent of the e-quotient. © 2008 Elsevier Inc. All rights reserved.