A local-global principle for unipotent characters
We obtain an adaptation of Dade’s Conjecture and Späth’s Character Triple Conjecture to unipotent characters of simple, simply connected finite reductive groups of type $\mathbf {A}$ , $\mathbf {B}$ and $\mathbf {C}$ . In particular, this gives a precise formula for counting the n...
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Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424000781/type/journal_article |
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| author | Damiano Rossi |
| author_facet | Damiano Rossi |
| author_sort | Damiano Rossi |
| collection | DOAJ |
| description | We obtain an adaptation of Dade’s Conjecture and Späth’s Character Triple Conjecture to unipotent characters of simple, simply connected finite reductive groups of type
$\mathbf {A}$
,
$\mathbf {B}$
and
$\mathbf {C}$
. In particular, this gives a precise formula for counting the number of unipotent characters of each defect d in any Brauer
$\ell $
-block B in terms of local invariants associated to e-local structures. This provides a geometric version of the local-global principle in representation theory of finite groups. A key ingredient in our proof is the construction of certain parametrisations of unipotent generalised Harish-Chandra series that are compatible with isomorphisms of character triples. |
| format | Article |
| id | doaj-art-b21a6f345ecc48348e95152ead8591c3 |
| institution | OA Journals |
| issn | 2050-5094 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-b21a6f345ecc48348e95152ead8591c32025-08-20T02:36:45ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2024.78A local-global principle for unipotent charactersDamiano Rossi0https://orcid.org/0000-0003-2832-2477FB Mathematik, RPTU Kaiserslautern–Landau, Postfach 3049, 67663 Kaiserslautern, Germany;We obtain an adaptation of Dade’s Conjecture and Späth’s Character Triple Conjecture to unipotent characters of simple, simply connected finite reductive groups of type $\mathbf {A}$ , $\mathbf {B}$ and $\mathbf {C}$ . In particular, this gives a precise formula for counting the number of unipotent characters of each defect d in any Brauer $\ell $ -block B in terms of local invariants associated to e-local structures. This provides a geometric version of the local-global principle in representation theory of finite groups. A key ingredient in our proof is the construction of certain parametrisations of unipotent generalised Harish-Chandra series that are compatible with isomorphisms of character triples.https://www.cambridge.org/core/product/identifier/S2050509424000781/type/journal_article20C2020C33 |
| spellingShingle | Damiano Rossi A local-global principle for unipotent characters Forum of Mathematics, Sigma 20C20 20C33 |
| title | A local-global principle for unipotent characters |
| title_full | A local-global principle for unipotent characters |
| title_fullStr | A local-global principle for unipotent characters |
| title_full_unstemmed | A local-global principle for unipotent characters |
| title_short | A local-global principle for unipotent characters |
| title_sort | local global principle for unipotent characters |
| topic | 20C20 20C33 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424000781/type/journal_article |
| work_keys_str_mv | AT damianorossi alocalglobalprincipleforunipotentcharacters AT damianorossi localglobalprincipleforunipotentcharacters |