The Jantzen sum formula for cyclotomic v-Schur algebras yields an identity for some q-analogues of the decomposition matrices of these algebras. We prove a similar identity for matrices of canonical bases of higher-level Fock spaces. We conjecture then that those matrices are actually identical for a suitable choice of parameters. In particular, we conjecture that decomposition matrices of cyclotomic v-Schur algebras are obtained by specializing at q = 1 some transition matrices between the standard basis and the canonical basis of a Fock space.
We show that the transition matrices between the standard and the canonical bases of infinitely many weight subspaces of the higher-level q-deformed Fock spaces are equal.
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