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

TL;DR

This paper extends the Leclerc-Thibon product theorem to higher level q-deformed Fock spaces under certain multi charge conditions, advancing the understanding of their algebraic structure.

Contribution

It provides a higher level analogue of the Leclerc-Thibon product theorem, generalizing previous results to more complex Fock space structures.

Findings

Established a higher level product theorem under multi charge conditions

Extended the formal q-analogue of tensor product theorems to higher levels

Contributed to the algebraic understanding of q-deformed Fock spaces

Abstract

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.