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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2604.01351 |
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| _version_ | 1866914439170621440 |
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| author | Linckelmann, Markus |
| author_facet | Linckelmann, Markus |
| contents | We show that the $p$-part of the conductor of a generalised character of a finite group is equal to the conductor of its generalised decomposition numbers. We use this to show that $p$-parts of conductors of irreducible characters are preserved under isotypies and perfect isometries that arise in the context of stable equivalences of Morita type with endopermutation source.
We apply this to blocks with abelian defect and Frobenius inertial quotient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01351 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the p-part of the conductor of a generalised character Linckelmann, Markus Representation Theory 20C15, 20C20, 20J05 We show that the $p$-part of the conductor of a generalised character of a finite group is equal to the conductor of its generalised decomposition numbers. We use this to show that $p$-parts of conductors of irreducible characters are preserved under isotypies and perfect isometries that arise in the context of stable equivalences of Morita type with endopermutation source. We apply this to blocks with abelian defect and Frobenius inertial quotient. |
| title | On the p-part of the conductor of a generalised character |
| topic | Representation Theory 20C15, 20C20, 20J05 |
| url | https://arxiv.org/abs/2604.01351 |