On the computation of the canonical basis for irreducible highest weight $U_q (\mathfrak{gl}_{\infty})$-module

Nicolas Jacon; Abel Lacabanne

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arXiv · 2601.16889

On the computation of the canonical basis for irreducible highest weight $U_q (\mathfrak{gl}_{\infty})$-module

Nicolas Jacon·Abel Lacabanne

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Abstract

We study canonical basis elements in higher-level Fock spaces associated with the quantum group $U_q(\mathfrak{gl}_\infty)$, which are conjecturally related to Calogero-Moser theory for complex reflection groups. We generalize the Leclerc-Miyachi formula to arbitrary levels by introducing new explicit constructions based on symbols, including a column removal theorem and closed formulas in several cases. These results provide explicit descriptions of canonical basis elements with applications to Calogero-Moser cellular characters and to the decomposition matrices of Ariki-Koike algebras.

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BibTeX RIS

Nicolas Jacon, Abel Lacabanne. 2026-01-23. On the computation of the canonical basis for irreducible highest weight $U_q (\mathfrak{gl}_{\infty})$-module. https://arxiv.org/abs/2601.16889

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