Rationality properties of complex representations of reductive p-adic groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915935025102848 |
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| author | Kazhdan, David Solleveld, Maarten Varshavsky, Yakov |
| author_facet | Kazhdan, David Solleveld, Maarten Varshavsky, Yakov |
| contents | For a reductive group G over a non-archimedean local field, we compare smooth representations over C with smooth representations over Qbar (an algebraic closure of Q). We show that an elliptic G-representation (in the sense of Arthur) can be realized over Qbar if and only if its central character takes values in Qbar. That applies in particular to all essentially square-integrable G-representations.
We also study the action of the automorphism group of C/Q on complex G-representations. We prove that the sets of essentially square-integrable representations and of elliptic representations are stable under Gal(C/Q). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rationality properties of complex representations of reductive p-adic groups Kazhdan, David Solleveld, Maarten Varshavsky, Yakov Representation Theory 20G25, 22E50 For a reductive group G over a non-archimedean local field, we compare smooth representations over C with smooth representations over Qbar (an algebraic closure of Q). We show that an elliptic G-representation (in the sense of Arthur) can be realized over Qbar if and only if its central character takes values in Qbar. That applies in particular to all essentially square-integrable G-representations. We also study the action of the automorphism group of C/Q on complex G-representations. We prove that the sets of essentially square-integrable representations and of elliptic representations are stable under Gal(C/Q). |
| title | Rationality properties of complex representations of reductive p-adic groups |
| topic | Representation Theory 20G25, 22E50 |
| url | https://arxiv.org/abs/2510.24201 |