  We obtain some simple relations between decomposition numbers of quantized
Schur algebras at an n-th root of unity (over a field of characteristic 0).
These relations imply that every decomposition number for such an algebra
occurs as a decomposition number for some Hecke algebra of type A. We prove
similar relations between coefficients of the canonical basis of the q-deformed
Fock space previously introduced in a joint work with Thibon. It follows that
these coefficients can all be expressed in terms of those of the global crystal
basis of the irreducible sub-representation generated by the vacuum vector. As
a consequence, using works of Ariki and Varagnolo-Vasserot, it is possible to
give a new proof of Lusztig's character formula for the simple
U_v(sl_r)-modules at roots of unity, which does not involve representations of
sl^_r of negative level.
