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

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

2011-02-09

arxiv.org/abs/1102.1780v3

Mathematics

Representation Theory

21 pages

Scientific paper

The q-deformed Fock spaces of higher levels were introduced by Jimbo-Misra-Miwa-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 $\ell$ coincides with that of level $\ell - 1$ under certain conditions of multi charge.

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