Galois automorphisms and blocks covering unipotent blocks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912907767316480 |
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| author | Ruhstorfer, L. Fry, A. A. Schaeffer |
| author_facet | Ruhstorfer, L. Fry, A. A. Schaeffer |
| contents | In this paper we prove that a recent condition of Lyons--Martínez--Navarro--Tiep, regarding the field of values of extensions of characters in principal blocks, is satisfied for all finite simple groups, which when combined with their results gives a new characterization of finite groups with a normal $\ell$-complement for a prime $\ell$. This leads us to study the distribution of characters in unipotent blocks of disconnected reductive groups and show that this is well-behaved under a generalization of $d$-Harish-Chandra theory. We go on to study the blockwise Galois--McKay (also known as the Alperin--McKay--Navarro) conjecture for the blocks of almost (quasi-)simple groups above unipotent blocks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_14902 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Galois automorphisms and blocks covering unipotent blocks Ruhstorfer, L. Fry, A. A. Schaeffer Representation Theory Group Theory 20C15, 20C33, 20C20 In this paper we prove that a recent condition of Lyons--Martínez--Navarro--Tiep, regarding the field of values of extensions of characters in principal blocks, is satisfied for all finite simple groups, which when combined with their results gives a new characterization of finite groups with a normal $\ell$-complement for a prime $\ell$. This leads us to study the distribution of characters in unipotent blocks of disconnected reductive groups and show that this is well-behaved under a generalization of $d$-Harish-Chandra theory. We go on to study the blockwise Galois--McKay (also known as the Alperin--McKay--Navarro) conjecture for the blocks of almost (quasi-)simple groups above unipotent blocks. |
| title | Galois automorphisms and blocks covering unipotent blocks |
| topic | Representation Theory Group Theory 20C15, 20C33, 20C20 |
| url | https://arxiv.org/abs/2602.14902 |