Aubert duals of strongly positive representations for metaplectic groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914223406186496 |
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| author | Kim, Yeansu Oh, Gyujin |
| author_facet | Kim, Yeansu Oh, Gyujin |
| contents | We determine the Aubert duals of strongly positive representations of the metaplectic group \(\widetilde{Sp}(n)\) over a non-Archimedean local field $F$ of characteristic different from two. Using the classification of Matić and an explicit analysis of Jacquet modules, we describe these duals in terms of precise inducing data. Our results extend known descriptions for classical groups to the metaplectic groups case and clarify the role of Aubert duality for non-linear covering groups, providing a foundation for future applications to the study of unitary representations for those cases. Furthermore, We are able to show that the same method applies to odd general spin groups $GSpin(2n+1)$, yielding an explicit description of Aubert duals in that setting as well. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Aubert duals of strongly positive representations for metaplectic groups Kim, Yeansu Oh, Gyujin Number Theory Representation Theory 22E35, 22E50, 11F70 We determine the Aubert duals of strongly positive representations of the metaplectic group \(\widetilde{Sp}(n)\) over a non-Archimedean local field $F$ of characteristic different from two. Using the classification of Matić and an explicit analysis of Jacquet modules, we describe these duals in terms of precise inducing data. Our results extend known descriptions for classical groups to the metaplectic groups case and clarify the role of Aubert duality for non-linear covering groups, providing a foundation for future applications to the study of unitary representations for those cases. Furthermore, We are able to show that the same method applies to odd general spin groups $GSpin(2n+1)$, yielding an explicit description of Aubert duals in that setting as well. |
| title | Aubert duals of strongly positive representations for metaplectic groups |
| topic | Number Theory Representation Theory 22E35, 22E50, 11F70 |
| url | https://arxiv.org/abs/2512.23218 |