Formal Degrees and Parabolic Induction: the Maximal Generic Case
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916849273274368 |
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| author | Wang, Yiyang |
| author_facet | Wang, Yiyang |
| contents | We study the compatibility of the formal degree conjecture and the parabolic induction process in the simplest nontrivial case for quasi-split $p$-adic groups. For a generic discrete series $π$ induced from an irreducible supercuspidal $σ$ of a maximal Levi subgroup, we compute the quotient $d(π)/d(σ)$ of formal degrees under some assumptions. As an application, we verify the conjecture for discrete series of split $\mathrm{G}_2$ supported on maximal Levi subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formal Degrees and Parabolic Induction: the Maximal Generic Case Wang, Yiyang Number Theory Representation Theory We study the compatibility of the formal degree conjecture and the parabolic induction process in the simplest nontrivial case for quasi-split $p$-adic groups. For a generic discrete series $π$ induced from an irreducible supercuspidal $σ$ of a maximal Levi subgroup, we compute the quotient $d(π)/d(σ)$ of formal degrees under some assumptions. As an application, we verify the conjecture for discrete series of split $\mathrm{G}_2$ supported on maximal Levi subgroups. |
| title | Formal Degrees and Parabolic Induction: the Maximal Generic Case |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2402.16456 |