The Hiraga-Ichino-Ikeda Conjecture for Principal Series of Split p-adic Groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913910313975808 |
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| author | Ricci, Giulio |
| author_facet | Ricci, Giulio |
| contents | Given a $p$-adic connected split reductive group $\mathcal{G},$ we use the local Langlands correspondence as defined by Reeder and by Aubert, Baum, Plymen and Solleveld, to prove the HII conjecture for irreducible discrete series representations contained in a principal series of $\mathcal{G}$. We verify the predicted formula relating the formal degree of such representations to the adjoint $γ$-factor of their associated Langlands parameter. First, we prove it under the assumption that the center of $\mathcal{G}$ is connected, and then we generalize the result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19619 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Hiraga-Ichino-Ikeda Conjecture for Principal Series of Split p-adic Groups Ricci, Giulio Representation Theory Number Theory 20C08, 22E50 Given a $p$-adic connected split reductive group $\mathcal{G},$ we use the local Langlands correspondence as defined by Reeder and by Aubert, Baum, Plymen and Solleveld, to prove the HII conjecture for irreducible discrete series representations contained in a principal series of $\mathcal{G}$. We verify the predicted formula relating the formal degree of such representations to the adjoint $γ$-factor of their associated Langlands parameter. First, we prove it under the assumption that the center of $\mathcal{G}$ is connected, and then we generalize the result. |
| title | The Hiraga-Ichino-Ikeda Conjecture for Principal Series of Split p-adic Groups |
| topic | Representation Theory Number Theory 20C08, 22E50 |
| url | https://arxiv.org/abs/2506.19619 |