On the character tables of the finite reductive groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916245177106432 |
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| author | Geck, Meinolf |
| author_facet | Geck, Meinolf |
| contents | We show how the character tables of the groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$ can be constructed, where $q$ is a power of~$2$. (Partial results are also obtained for any $q$ not divisible by~$3$.) This is based on previous work by Hetz, Lusztig, Malle, Mizuno and Shoji, plus computations using Michel's version of {\sf CHEVIE}. We also need some general results that are specific to semisimple groups which are not of simply connected type. A further crucial ingredient is the determination of the values of the unipotent characters on unipotent elements for groups of type $D_4$ and $D_5$ (in characteristic~$2$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the character tables of the finite reductive groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$ Geck, Meinolf Representation Theory Primary 20C33, secondary 20G40 We show how the character tables of the groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$ can be constructed, where $q$ is a power of~$2$. (Partial results are also obtained for any $q$ not divisible by~$3$.) This is based on previous work by Hetz, Lusztig, Malle, Mizuno and Shoji, plus computations using Michel's version of {\sf CHEVIE}. We also need some general results that are specific to semisimple groups which are not of simply connected type. A further crucial ingredient is the determination of the values of the unipotent characters on unipotent elements for groups of type $D_4$ and $D_5$ (in characteristic~$2$). |
| title | On the character tables of the finite reductive groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$ |
| topic | Representation Theory Primary 20C33, secondary 20G40 |
| url | https://arxiv.org/abs/2403.02434 |