Sign sequences and decomposition numbers

Abstract

We obtain a closed formula for the ν-decomposition numbers dλμ(ν) arising from the canonical basis of the Fock space representation of Uν(sle), where the partition λ is obtained from μ by moving some nodes in its Young diagram, all of which have the same e-residue. We also show that when these ν-decomposition numbers are evaluated at ν = 1, we obtain the corresponding decomposition numbers for the Schur algebras and symmetric groups. © 2013 American Mathematical Society.