arXiv subjects

Giulio Ricci

Publications and source records attributed to Giulio Ricci.

2 recordsLinked to original sources

arXiv2026

Formal degree of principal series of quasi-split groups

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.

math.RT↗

arXiv2025

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

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.

math.RT↗