The B(G)-parametrization of the local Langlands correspondence
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914079787974656 |
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| author | Meli, Alexander Bertoloni Oi, Masao |
| author_facet | Meli, Alexander Bertoloni Oi, Masao |
| contents | This article is on the parametrization of the local Langlands correspondence over local fields for non-quasi-split groups according to the philosophy of Vogan. We show that a parametrization indexed by the basic part of the Kottwitz set (which is an extension of the set of pure inner twists) implies a parametrization indexed by the full Kottwitz set. On the Galois side, we consider irreducible algebraic representations of the full centralizer group of the $L$-parameter (i.e not a component group). When $F$ is a $p$-adic field, we discuss a generalization of the endoscopic character identity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_13864 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The B(G)-parametrization of the local Langlands correspondence Meli, Alexander Bertoloni Oi, Masao Number Theory Representation Theory 22E50, 11S37, 11F70 This article is on the parametrization of the local Langlands correspondence over local fields for non-quasi-split groups according to the philosophy of Vogan. We show that a parametrization indexed by the basic part of the Kottwitz set (which is an extension of the set of pure inner twists) implies a parametrization indexed by the full Kottwitz set. On the Galois side, we consider irreducible algebraic representations of the full centralizer group of the $L$-parameter (i.e not a component group). When $F$ is a $p$-adic field, we discuss a generalization of the endoscopic character identity. |
| title | The B(G)-parametrization of the local Langlands correspondence |
| topic | Number Theory Representation Theory 22E50, 11S37, 11F70 |
| url | https://arxiv.org/abs/2211.13864 |