An equivariant bijection of irreducible Brauer characters above the Dade-Glauberman-Nagao correspondence
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913883540684800 |
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| author | Fu, Qulei |
| author_facet | Fu, Qulei |
| contents | The Glauberman correspondence and its generalisation, the Dade--Glauberman--Nagao (DGN) correspondence, play an important role in studying local-global counting conjectures and their reductions to (quasi-)simple groups. These reduction theorems require an additional set of compatibility conditions for the DGN correspondence. In this paper, we prove that there exists a bijection of irreducible Brauer characters above the DGN correspondence that is equivariant with Galois automorphisms and group automorphisms and preserves vertices. Our proof utilizes the framework of $\hH$-triples developed by Navarro--Späth--Vallejo. The results establish a reduction theorem for the Galois Alperin weight conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06471 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An equivariant bijection of irreducible Brauer characters above the Dade-Glauberman-Nagao correspondence Fu, Qulei Group Theory The Glauberman correspondence and its generalisation, the Dade--Glauberman--Nagao (DGN) correspondence, play an important role in studying local-global counting conjectures and their reductions to (quasi-)simple groups. These reduction theorems require an additional set of compatibility conditions for the DGN correspondence. In this paper, we prove that there exists a bijection of irreducible Brauer characters above the DGN correspondence that is equivariant with Galois automorphisms and group automorphisms and preserves vertices. Our proof utilizes the framework of $\hH$-triples developed by Navarro--Späth--Vallejo. The results establish a reduction theorem for the Galois Alperin weight conjecture. |
| title | An equivariant bijection of irreducible Brauer characters above the Dade-Glauberman-Nagao correspondence |
| topic | Group Theory |
| url | https://arxiv.org/abs/2311.06471 |