Vogan's Conjecture on local Arthur packets of $p$-adic $\mathrm{GL}_n$ and a combinatorial Lemma
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915085599899648 |
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| author | Lo, Chi-Heng |
| author_facet | Lo, Chi-Heng |
| contents | For $\mathrm{GL}_n$ over a $p$-adic field, Cunningham and Ray proved Vogan's conjecture, that is, local Arthur packets are the same as ABV packets. They used the endoscopic theory to reduce the general case to a combinatorial lemma for irreducible local Arthur parameters, and their proof implies that one can also prove Vogan's conjecture for $p$-adic $\mathrm{GL}_n$ by proving a generalized version of this combinatorial lemma. Riddlesden recently proved this generalized lemma. In this paper, we give a new proof of it, which has its own interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00249 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vogan's Conjecture on local Arthur packets of $p$-adic $\mathrm{GL}_n$ and a combinatorial Lemma Lo, Chi-Heng Representation Theory Number Theory For $\mathrm{GL}_n$ over a $p$-adic field, Cunningham and Ray proved Vogan's conjecture, that is, local Arthur packets are the same as ABV packets. They used the endoscopic theory to reduce the general case to a combinatorial lemma for irreducible local Arthur parameters, and their proof implies that one can also prove Vogan's conjecture for $p$-adic $\mathrm{GL}_n$ by proving a generalized version of this combinatorial lemma. Riddlesden recently proved this generalized lemma. In this paper, we give a new proof of it, which has its own interest. |
| title | Vogan's Conjecture on local Arthur packets of $p$-adic $\mathrm{GL}_n$ and a combinatorial Lemma |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2311.00249 |