The Hiraga-Ichino-Ikeda Conjecture for Principal Series of Split p-adic Groups

Fuente: arXiv
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Autore principale: Ricci, Giulio
Natura: Preprint
Pubblicazione: 2025
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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