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

2025/06/24 by Ricci, Giulio · 1 citation
Mathematics · #20C08 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.19619

openalex publication_date 2025/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Formal degree of principal series of quasi-split groups

Related

• Extended quotients in the principal series of reductive p-adic groups
• Geometric structure and the local Langlands conjecture
• Formal degree of principal series of quasi-split groups
• Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda
• Rigid vectors in p-adic principal series representations