Standard modules and intertwining operators for reductive p-adic groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914213051498496 |
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| author | Solleveld, Maarten |
| author_facet | Solleveld, Maarten |
| contents | Consider a reductive group G over a non-archimedean local field. The Galois group Gal(C/Q) acts naturally on the category of smooth complex G-representations. We prove that this action stabilizes the class of standard modules. This generalizes and relies on an analogous result about essentially square-integrable representations.
Other important objects in the proof of our main result are intertwining operators between parabolically induced G-representations, and the associated Harish-Chandra μ-functions. We determine an explicit formula for the μ-function of any irreducible representation of any Levi subgroup of G. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Standard modules and intertwining operators for reductive p-adic groups Solleveld, Maarten Representation Theory 20G25, 22E50, 22E30 Consider a reductive group G over a non-archimedean local field. The Galois group Gal(C/Q) acts naturally on the category of smooth complex G-representations. We prove that this action stabilizes the class of standard modules. This generalizes and relies on an analogous result about essentially square-integrable representations. Other important objects in the proof of our main result are intertwining operators between parabolically induced G-representations, and the associated Harish-Chandra μ-functions. We determine an explicit formula for the μ-function of any irreducible representation of any Levi subgroup of G. |
| title | Standard modules and intertwining operators for reductive p-adic groups |
| topic | Representation Theory 20G25, 22E50, 22E30 |
| url | https://arxiv.org/abs/2512.18685 |