Canonical bases for Fock spaces and tensor products

We relate the canonical basis of the Fock space representation of the quantum affine algebra Uq(glˆn), as defined by Leclerc and Thibon [15], to the canonical basis of its restriction to Uq(sln), regarded as a based module in the sense of Lusztig. More generally we consider the restriction to any Levi subalgebra. We deduce results on decomposition numbers and branching coefficients of Schur algebras over fields of positive characteristic, generalizing those of Kleshchev [13] and of Tan and Teo [19].