On principal series representations of quasi-split reductive p-adic groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909486296334336 |
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| author | Solleveld, Maarten |
| author_facet | Solleveld, Maarten |
| contents | Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and its image is an explicitly described set of enhanced L-parameters. Our correspondence is determined by the choice of a Whittaker datum for G, and it is canonical given that choice.
We show that our parametrization satisfies many expected properties, among others with respect to the enhanced L-parameters of generic representations, temperedness, cuspidal supports and central characters. Along the way we characterize genericity in terms of representations of an affine Hecke algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06418 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On principal series representations of quasi-split reductive p-adic groups Solleveld, Maarten Representation Theory 22E50, 20C08, 20G25 Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and its image is an explicitly described set of enhanced L-parameters. Our correspondence is determined by the choice of a Whittaker datum for G, and it is canonical given that choice. We show that our parametrization satisfies many expected properties, among others with respect to the enhanced L-parameters of generic representations, temperedness, cuspidal supports and central characters. Along the way we characterize genericity in terms of representations of an affine Hecke algebra. |
| title | On principal series representations of quasi-split reductive p-adic groups |
| topic | Representation Theory 22E50, 20C08, 20G25 |
| url | https://arxiv.org/abs/2304.06418 |