A local-global principle for unipotent characters
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917870531772416 |
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| author | Rossi, Damiano |
| author_facet | Rossi, Damiano |
| contents | 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 $\bf{A}$, $\bf{B}$ and $\bf{C}$. 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05151 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A local-global principle for unipotent characters Rossi, Damiano Representation Theory Group Theory 20C20, 20C33 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 $\bf{A}$, $\bf{B}$ and $\bf{C}$. 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. |
| title | A local-global principle for unipotent characters |
| topic | Representation Theory Group Theory 20C20, 20C33 |
| url | https://arxiv.org/abs/2301.05151 |