Generalized Green functions and unipotent classes for finite reductive groups, IV
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909301320187904 |
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| author | Lübeck, Frank Shoji, Toshiaki |
| author_facet | Lübeck, Frank Shoji, Toshiaki |
| contents | In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group $G$. Generalized Green functions of $G$ can be computed by using Lusztig's algorithm, if split elements exist for any unipotent class. The existence of split elements is reduced to the case where $G$ is a simply connected, almost simple group. We show, in the case of classical groups, split elements exist, which is a refinement of previous results. In the case of exceptional groups, we show the existence of split elements, possibly except one class for $G$ of type $E_7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16960 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Green functions and unipotent classes for finite reductive groups, IV Lübeck, Frank Shoji, Toshiaki Representation Theory 20G05, 20G40 In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group $G$. Generalized Green functions of $G$ can be computed by using Lusztig's algorithm, if split elements exist for any unipotent class. The existence of split elements is reduced to the case where $G$ is a simply connected, almost simple group. We show, in the case of classical groups, split elements exist, which is a refinement of previous results. In the case of exceptional groups, we show the existence of split elements, possibly except one class for $G$ of type $E_7$. |
| title | Generalized Green functions and unipotent classes for finite reductive groups, IV |
| topic | Representation Theory 20G05, 20G40 |
| url | https://arxiv.org/abs/2408.16960 |