Supercuspidal representations: construction, classification, and characters
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911210862018560 |
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| author | Fintzen, Jessica |
| author_facet | Fintzen, Jessica |
| contents | The building blocks for irreducible smooth representations of p-adic groups are the supercuspidal representations. In these notes that are an expansion of a lecture series given during the IHES summer school 2022 we will explore an explicit exhaustive construction of these supercuspidal representations and their character formulas and observe a striking parallel between a large class of these representations and discrete series representations of real algebraic Lie groups. A key ingredient for the construction of supercuspidal representations is the Bruhat-Tits theory and Moy-Prasad filtration, which we will recall in this survey. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12883 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supercuspidal representations: construction, classification, and characters Fintzen, Jessica Representation Theory Number Theory The building blocks for irreducible smooth representations of p-adic groups are the supercuspidal representations. In these notes that are an expansion of a lecture series given during the IHES summer school 2022 we will explore an explicit exhaustive construction of these supercuspidal representations and their character formulas and observe a striking parallel between a large class of these representations and discrete series representations of real algebraic Lie groups. A key ingredient for the construction of supercuspidal representations is the Bruhat-Tits theory and Moy-Prasad filtration, which we will recall in this survey. |
| title | Supercuspidal representations: construction, classification, and characters |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2510.12883 |