Abstract
We obtain closed formulas, in terms of Littlewood–Richardson coefficients, for the canonical basis elements of the Fock space representation of U v ( sl ˆ 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.
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