Principal blocks, irreducible restriction, fields and degrees
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908477597679616 |
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| author | Lyons, Richard Martínez, J. Miquel Navarro, Gabriel Tiep, Pham Huu |
| author_facet | Lyons, Richard Martínez, J. Miquel Navarro, Gabriel Tiep, Pham Huu |
| contents | Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ alternative group-theoretical techniques to address the "going down" case. This approach enables us to reduce the block version of well-known results by the third and fourth authors to a question about almost simple groups. Moreover, this suggests a Galois analogue of the height-zero-equal-degree conjecture of Malle and Navarro, which we formulate. However, the "going up" case of irreducible extensions of principal block characters remains unresolved. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Principal blocks, irreducible restriction, fields and degrees Lyons, Richard Martínez, J. Miquel Navarro, Gabriel Tiep, Pham Huu Representation Theory Primary 20D20, Secondary 20C15 Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ alternative group-theoretical techniques to address the "going down" case. This approach enables us to reduce the block version of well-known results by the third and fourth authors to a question about almost simple groups. Moreover, this suggests a Galois analogue of the height-zero-equal-degree conjecture of Malle and Navarro, which we formulate. However, the "going up" case of irreducible extensions of principal block characters remains unresolved. |
| title | Principal blocks, irreducible restriction, fields and degrees |
| topic | Representation Theory Primary 20D20, Secondary 20C15 |
| url | https://arxiv.org/abs/2507.22503 |