On the upper bound of wavefront sets of representations of p-adic groups
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910191080964096 |
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| author | Hazeltine, Alexander Liu, Baiying Lo, Chi-Heng Shahidi, Freydoon |
| author_facet | Hazeltine, Alexander Liu, Baiying Lo, Chi-Heng Shahidi, Freydoon |
| contents | In this paper we study the upper bound of wavefront sets of irreducible admissible representations of connected reductive groups defined over non-Archimedean local fields of characteristic zero. We formulate a new conjecture on the upper bound and show that it can be reduced to that of anti-discrete series representations, namely, those whose Aubert-Zelevinsky duals are discrete series. Then, we show that this conjecture is equivalent to the Jiang conjecture on the upper bound of wavefront sets of representations in local Arthur packets and also equivalent to an analogous conjecture on the upper bound of wavefront sets of representations in local ABV packets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11976 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the upper bound of wavefront sets of representations of p-adic groups Hazeltine, Alexander Liu, Baiying Lo, Chi-Heng Shahidi, Freydoon Representation Theory Number Theory In this paper we study the upper bound of wavefront sets of irreducible admissible representations of connected reductive groups defined over non-Archimedean local fields of characteristic zero. We formulate a new conjecture on the upper bound and show that it can be reduced to that of anti-discrete series representations, namely, those whose Aubert-Zelevinsky duals are discrete series. Then, we show that this conjecture is equivalent to the Jiang conjecture on the upper bound of wavefront sets of representations in local Arthur packets and also equivalent to an analogous conjecture on the upper bound of wavefront sets of representations in local ABV packets. |
| title | On the upper bound of wavefront sets of representations of p-adic groups |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2403.11976 |