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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2604.14823 |
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| _version_ | 1866913038196539392 |
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| author | Ricci, Giulio |
| author_facet | Ricci, Giulio |
| contents | Let $\mathcal{G}$ be a quasi-split connected reductive group over a non-archimedean local field $F.$ In this paper, we prove the formal degree conjecture for discrete series representations contained in a principal series of $\mathcal{G}(F)$. We first construct a type for each Bernstein component attached to a principal series representation of $\mathcal{G}(F).$ We then use these types and the local Langlands correspondence for principal series representations defined in [Sol25] to verify the formal degree conjecture. Our approach follows a similar strategy to [Ric25], reducing the problem to the case of unipotent representations of some other quasi-split group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14823 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Formal degree of principal series of quasi-split groups Ricci, Giulio Representation Theory 22E50 (Primary) 20C08, 20G25 (Secondary) Let $\mathcal{G}$ be a quasi-split connected reductive group over a non-archimedean local field $F.$ In this paper, we prove the formal degree conjecture for discrete series representations contained in a principal series of $\mathcal{G}(F)$. We first construct a type for each Bernstein component attached to a principal series representation of $\mathcal{G}(F).$ We then use these types and the local Langlands correspondence for principal series representations defined in [Sol25] to verify the formal degree conjecture. Our approach follows a similar strategy to [Ric25], reducing the problem to the case of unipotent representations of some other quasi-split group. |
| title | Formal degree of principal series of quasi-split groups |
| topic | Representation Theory 22E50 (Primary) 20C08, 20G25 (Secondary) |
| url | https://arxiv.org/abs/2604.14823 |