Sign sequences and decomposition numbers

Abstract

We obtain a closed formula for the v-decomposition numbers dλμ(v) arising from the canonical basis of the Fock space representation of Uv(ŝle), where the partition λ is obtained from μ by moving some nodes in its Young diagram, all of which having the same e-residue. We also show that when these v-decomposition numbers are evaluated at v = 1, we obtain the corresponding decomposition numbers for the Schur algebras and symmetric groups.