On a higher level extension of Leclerc-Thibon product theorem in q-deformed Fock spaces

The q-deformed Fock spaces of higher levels were introduced by Jimbo-Misra-Miwa-Okado. Uglov defined a canonical bases in q-deformed Fock spaces of higher levels. Leclerc-Thibon showed a product theorem in q-deformed Fock spaces of level one. The product theorem is regarded as a formal $q$-analogue of the tensor product theorem of level one. In this paper, we show a higher level analogue of Leclerc-Thibon product theorem under a suitable multi charge condition.