A comparison of q-decomposition numbers in the q-deformed Fock spaces of higher levels

The q-deformed Fock spaces of higher levels were introduced by Jimbo, Misra, Miwa and Okado. The q-decomposition matrix is a transition matrix from the standard basis to the canonical basis defined by Uglov in the q-deformed Fock space. In this paper, we show that parts of q-decomposition matrices of level ℓ coincide with that of level ℓ−1 under certain conditions of multicharge.