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

TL;DR

This paper investigates the structure of q-decomposition matrices in higher-level q-deformed Fock spaces, revealing conditions under which matrices of different levels coincide, thus advancing understanding of their algebraic properties.

Contribution

It establishes a connection between q-decomposition matrices of different levels under specific multi charge conditions, providing new insights into their structure.

Findings

Parts of q-decomposition matrices of level ℓ match those of level ℓ-1 under certain conditions.

The results clarify the relationship between different levels in q-deformed Fock spaces.

The study enhances understanding of the algebraic structure of q-decomposition matrices.

Abstract

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.