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In our earlier work, we have proved a product formula for certaindecomposition numbers of the cyclotomic v-Schur algebra associated to theAriki-Koike algebra. It is conjectured by Yvonne that the decomposition numbersof this algebra can be described in terms of the canonical basis of the higherlevel Fock space studied by Uglov. In this paper we prove a product formularelated to the canonical basis of the Fock space. In view of Yvonne'sconjecture, this formula is regarded as a counter-part for the Fock space ofour previous formula.

Product formulas for the cyclotomic v-Schur algebra and for the canonical bases of the Fock space