Fusion systems related to polynomial representations of $\mathrm{SL}_2(q)$
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915765175713792 |
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| author | Grazian, Valentina Parker, Chris Semeraro, Jason van Beek, Martin |
| author_facet | Grazian, Valentina Parker, Chris Semeraro, Jason van Beek, Martin |
| contents | Let $q$ be a power of a fixed prime $p$. We classify up to isomorphism all simple saturated fusion systems on a certain class of $p$-groups constructed from the polynomial representations of $\mathrm{SL}_2(q)$, which includes the Sylow $p$-subgroups of $\mathrm{GL}_3(q)$ and $\mathrm{Sp}_4(q)$ as special cases. The resulting list includes all Clelland--Parker fusion systems, a simple exotic fusion system discovered by Henke--Shpectorov, and a new infinite family of exotic examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20873 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fusion systems related to polynomial representations of $\mathrm{SL}_2(q)$ Grazian, Valentina Parker, Chris Semeraro, Jason van Beek, Martin Group Theory Representation Theory 20D20, 20D05, 20E42, 20C33 Let $q$ be a power of a fixed prime $p$. We classify up to isomorphism all simple saturated fusion systems on a certain class of $p$-groups constructed from the polynomial representations of $\mathrm{SL}_2(q)$, which includes the Sylow $p$-subgroups of $\mathrm{GL}_3(q)$ and $\mathrm{Sp}_4(q)$ as special cases. The resulting list includes all Clelland--Parker fusion systems, a simple exotic fusion system discovered by Henke--Shpectorov, and a new infinite family of exotic examples. |
| title | Fusion systems related to polynomial representations of $\mathrm{SL}_2(q)$ |
| topic | Group Theory Representation Theory 20D20, 20D05, 20E42, 20C33 |
| url | https://arxiv.org/abs/2502.20873 |