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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.03552 |
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| _version_ | 1866916472090001408 |
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| author | Adams, Jeffrey Afgoustidis, Alexandre |
| author_facet | Adams, Jeffrey Afgoustidis, Alexandre |
| contents | Consider the irreducible representations of a real reductive group $G(\mathbb{R})$, and their parametrization by the local Langlands correspondence. We ask: does the parametrization give easily accessible information on the restriction of representations to a maximal compact subgroup $K(\mathbb{R})$ of $G(\mathbb{R})$? We find a natural connection between the set of lowest $K$-types of a representation and its Langlands parameters.
For our results, it is crucial to use the refined version of the local Langlands correspondence, involving (coverings of) component groups attached to $L$-homomorphisms. The first part of the paper is a simplified description of this refined parametrization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lowest $K$-types in the local Langlands correspondence Adams, Jeffrey Afgoustidis, Alexandre Representation Theory 22E47, 22E50, 20G05 Consider the irreducible representations of a real reductive group $G(\mathbb{R})$, and their parametrization by the local Langlands correspondence. We ask: does the parametrization give easily accessible information on the restriction of representations to a maximal compact subgroup $K(\mathbb{R})$ of $G(\mathbb{R})$? We find a natural connection between the set of lowest $K$-types of a representation and its Langlands parameters. For our results, it is crucial to use the refined version of the local Langlands correspondence, involving (coverings of) component groups attached to $L$-homomorphisms. The first part of the paper is a simplified description of this refined parametrization. |
| title | Lowest $K$-types in the local Langlands correspondence |
| topic | Representation Theory 22E47, 22E50, 20G05 |
| url | https://arxiv.org/abs/2402.03552 |