Irreducible projective representations of the symmetric group which remain irreducible in characteristic $2$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866910298556858368 |
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| author | Fayers, Matthew |
| author_facet | Fayers, Matthew |
| contents | For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our techniques involve constructing part of the decomposition matrix for a Rouquier block of a double cover, restricting to subgroups using the Brundan--Kleshchev modular branching rules and comparing the dimensions of irreducible representations via the bar-length formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1608_04502 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Irreducible projective representations of the symmetric group which remain irreducible in characteristic $2$ Fayers, Matthew Representation Theory 20C30, 20C25, 05E10 For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our techniques involve constructing part of the decomposition matrix for a Rouquier block of a double cover, restricting to subgroups using the Brundan--Kleshchev modular branching rules and comparing the dimensions of irreducible representations via the bar-length formula. |
| title | Irreducible projective representations of the symmetric group which remain irreducible in characteristic $2$ |
| topic | Representation Theory 20C30, 20C25, 05E10 |
| url | https://arxiv.org/abs/1608.04502 |