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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.13332 |
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| _version_ | 1866910383805038592 |
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| author | Huang, Xin |
| author_facet | Huang, Xin |
| contents | We extend a theorem of Kessar and Linckelmann concerning Morita equivalences and Brauer character bijections between blocks to virtual Morita equivalences. As a corollary, we obtain that Navarro's refinement of Alperin's weight conjecture holds for blocks with cyclic and Klein four defect groups, blocks of symmetric and alternating groups with abelian defect groups, and $p$-blocks of ${\rm SL}_2(q)$ and ${\rm GL}_2(q)$, where $p|q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Virtual Morita equivalences and Brauer character bijections Huang, Xin Representation Theory We extend a theorem of Kessar and Linckelmann concerning Morita equivalences and Brauer character bijections between blocks to virtual Morita equivalences. As a corollary, we obtain that Navarro's refinement of Alperin's weight conjecture holds for blocks with cyclic and Klein four defect groups, blocks of symmetric and alternating groups with abelian defect groups, and $p$-blocks of ${\rm SL}_2(q)$ and ${\rm GL}_2(q)$, where $p|q$. |
| title | Virtual Morita equivalences and Brauer character bijections |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2401.13332 |