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This is a Quantitative Study study.

October 2, 2025Open Access

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

Key Points

The HII conjecture is validated for discrete series representations in the context of p-adic groups.
A formula connecting the formal degree of representations to the adjoint γ-factor was successfully verified.
The findings first required the center of the group to be connected before generalizations were made.
The study employs the local Langlands correspondence, crucial for the conjecture's proof.

Abstract

Given a p-adic connected split reductive group 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 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 G is connected, and then we generalize the result.

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Cite This Study

Giovanni Ricci (Tue,) studied this question.

synapsesocial.com/papers/68de84bf5b556a9128e1bf2b https://doi.org/https://doi.org/10.48550/arxiv.2506.19619

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