Local coefficients and Gelfand-Graev representations for non-split covers on SL(2)
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917645885898752 |
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| author | Jo, Yeongseong |
| author_facet | Jo, Yeongseong |
| contents | A purely local approach has been developed by Krishnamurthy and Kutzko to compute Langlands-Shahidi local coefficient for ${\rm SL}(2)$ via types and covers à la Bushnell-Kutzko. In this paper, we extend their method to the non-split case and complete their project. We also study the algebraic structure of Gelfand-Graev representations, which generalizes the results of Chan-Savin and Mishra-Pattanayak to ${\rm SL}(2)$ over non-archimidean local fields without any restriction on the characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12378 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Local coefficients and Gelfand-Graev representations for non-split covers on SL(2) Jo, Yeongseong Number Theory Representation Theory A purely local approach has been developed by Krishnamurthy and Kutzko to compute Langlands-Shahidi local coefficient for ${\rm SL}(2)$ via types and covers à la Bushnell-Kutzko. In this paper, we extend their method to the non-split case and complete their project. We also study the algebraic structure of Gelfand-Graev representations, which generalizes the results of Chan-Savin and Mishra-Pattanayak to ${\rm SL}(2)$ over non-archimidean local fields without any restriction on the characteristic. |
| title | Local coefficients and Gelfand-Graev representations for non-split covers on SL(2) |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2209.12378 |