Non-basic rigid packets for discrete $L$-parameters
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916369504665600 |
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| author | Dillery, Peter Schwein, David |
| author_facet | Dillery, Peter Schwein, David |
| contents | This article introduces the theory of non-basic rigid inner forms over $p$-adic local fields, extending the basic theory developed by Kaletha. Motivated by the recent work of Bertoloni Meli--Oi on the $B(G)$-parametrization of the local Langlands conjectures, our main application is to extend the basic rigid refined local Langlands conjectures for a discrete $L$-parameter $ϕ$ of a quasi-split connected reductive group $G$. The packets of our extended construction are Weyl orbits of representations of inner forms of twisted Levi subgroups $N$ of $G$ for which $ϕ$ factors through a member of the canonical $\widehat{G}$-conjugacy class of embeddings $^{L}N_{\pm} \to \hspace{1mm} ^{L}G$ constructed by Kaletha. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_13908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-basic rigid packets for discrete $L$-parameters Dillery, Peter Schwein, David Number Theory Representation Theory 11R39, 11E72, 22E50 This article introduces the theory of non-basic rigid inner forms over $p$-adic local fields, extending the basic theory developed by Kaletha. Motivated by the recent work of Bertoloni Meli--Oi on the $B(G)$-parametrization of the local Langlands conjectures, our main application is to extend the basic rigid refined local Langlands conjectures for a discrete $L$-parameter $ϕ$ of a quasi-split connected reductive group $G$. The packets of our extended construction are Weyl orbits of representations of inner forms of twisted Levi subgroups $N$ of $G$ for which $ϕ$ factors through a member of the canonical $\widehat{G}$-conjugacy class of embeddings $^{L}N_{\pm} \to \hspace{1mm} ^{L}G$ constructed by Kaletha. |
| title | Non-basic rigid packets for discrete $L$-parameters |
| topic | Number Theory Representation Theory 11R39, 11E72, 22E50 |
| url | https://arxiv.org/abs/2408.13908 |