On the computation of the canonical basis for irreducible highest weight $U_q (\mathfrak{gl}_{\infty})$-module
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912843943641088 |
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| author | Jacon, Nicolas Lacabanne, Abel |
| author_facet | Jacon, Nicolas Lacabanne, Abel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_16889 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the computation of the canonical basis for irreducible highest weight $U_q (\mathfrak{gl}_{\infty})$-module Jacon, Nicolas Lacabanne, Abel Representation Theory Quantum Algebra 05E10, 17B37, 20C08 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. |
| title | On the computation of the canonical basis for irreducible highest weight $U_q (\mathfrak{gl}_{\infty})$-module |
| topic | Representation Theory Quantum Algebra 05E10, 17B37, 20C08 |
| url | https://arxiv.org/abs/2601.16889 |