Jordan correspondence and block distribution of characters
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915147086299136 |
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| author | Kessar, Radha Malle, Gunter |
| author_facet | Kessar, Radha Malle, Gunter |
| contents | We complete the determination of the $\ell$-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the $\ell$-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from $\ell$ has connected centre. As a consequence we derive a compatibility between $\ell$-blocks, $e$-Harish-Chandra series and Jordan decomposition. Further we apply our results to complete the proof of Robinson's conjecture on defects of characters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13510 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Jordan correspondence and block distribution of characters Kessar, Radha Malle, Gunter Representation Theory Group Theory 20C15, 20C20, 20C33 We complete the determination of the $\ell$-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the $\ell$-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from $\ell$ has connected centre. As a consequence we derive a compatibility between $\ell$-blocks, $e$-Harish-Chandra series and Jordan decomposition. Further we apply our results to complete the proof of Robinson's conjecture on defects of characters. |
| title | Jordan correspondence and block distribution of characters |
| topic | Representation Theory Group Theory 20C15, 20C20, 20C33 |
| url | https://arxiv.org/abs/2311.13510 |