Galois Automorphisms and Classical Groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866913504692273152 |
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| author | Fry, A. A. Schaeffer Taylor, Jay |
| author_facet | Fry, A. A. Schaeffer Taylor, Jay |
| contents | In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the finite symplectic groups. We generalise this in two directions. Firstly, using work of the first-named author, we give a complete description of the action of Galois automorphisms on irreducible characters. Secondly, we extend both descriptions to cover the case of special orthogonal groups. As a consequence, we obtain explicit descriptions for the character fields of symplectic and special orthogonal groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_14088 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Galois Automorphisms and Classical Groups Fry, A. A. Schaeffer Taylor, Jay Representation Theory Primary 20C30, Secondary 20C15 In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the finite symplectic groups. We generalise this in two directions. Firstly, using work of the first-named author, we give a complete description of the action of Galois automorphisms on irreducible characters. Secondly, we extend both descriptions to cover the case of special orthogonal groups. As a consequence, we obtain explicit descriptions for the character fields of symplectic and special orthogonal groups. |
| title | Galois Automorphisms and Classical Groups |
| topic | Representation Theory Primary 20C30, Secondary 20C15 |
| url | https://arxiv.org/abs/2005.14088 |