Inductive local-global conditions and generalised Harish-Chandra theory
We study new properties of generalised Harish-Chandra theory aiming at explaining the inductive local-global conditions for finite groups of Lie type in nondefining characteristic. In particular, we consider a parametrisation of generalised Harish-Chandra series that is compatible with Clifford theo...
| Published in: | Forum of Mathematics, Sigma |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Cambridge University Press
2025-01-01
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| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425101151/type/journal_article |
| Summary: | We study new properties of generalised Harish-Chandra theory aiming at explaining the inductive local-global conditions for finite groups of Lie type in nondefining characteristic. In particular, we consider a parametrisation of generalised Harish-Chandra series that is compatible with Clifford theory and with the action of automorphisms on irreducible characters and we reduce it to the verification of certain requirements on stabilisers and extendibility of characters. This parametrisation is used by the author in a separate paper to obtain new conjectures for finite reductive groups that can be seen as geometric realisations of the local-global counting conjectures and their inductive conditions. As a by-product, we extend the parametrisation of generalised Harish-Chandra series given by Broué–Malle–Michel to the nonunipotent case by assuming maximal extendibility. |
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| ISSN: | 2050-5094 |