Weight conjectures for Parker--Semeraro fusion systems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917717505736704 |
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| author | Kessar, Radha Semeraro, Jason Serwene, Patrick Tuvay, İpek |
| author_facet | Kessar, Radha Semeraro, Jason Serwene, Patrick Tuvay, İpek |
| contents | We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal $3$-block of Aut$(G_2(3))$, the principal $5$-blocks of $HN$, $BM$, Aut$(HN)$, $Ly$, the principal $7$-block of $M$, and the principal $p$-blocks of $G_2(p)$ for $p\geq 3 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07211 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weight conjectures for Parker--Semeraro fusion systems Kessar, Radha Semeraro, Jason Serwene, Patrick Tuvay, İpek Representation Theory Group Theory 20D45, 20C05 We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal $3$-block of Aut$(G_2(3))$, the principal $5$-blocks of $HN$, $BM$, Aut$(HN)$, $Ly$, the principal $7$-block of $M$, and the principal $p$-blocks of $G_2(p)$ for $p\geq 3 $. |
| title | Weight conjectures for Parker--Semeraro fusion systems |
| topic | Representation Theory Group Theory 20D45, 20C05 |
| url | https://arxiv.org/abs/2407.07211 |