The FPP Conjecture for p-adic Groups

2025/09/22 by Jiang, Dihua, Liu, Baiying, Lo, Chi-Heng +1 · 1 citation
#22E50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.18320

Abstract

The FPP conjecture, proposed by J. Adams, S. Miller, and D. Vogan and proved by D. Davis and L. Mason-Brown in arXiv:2411.01372, imposes a strong upper bound on the infinitesimal character of a unitary representation of a real reductive group. In this paper, we formulate an analogous conjecture for p-adic groups. We prove our conjecture for pure rational forms assuming a version of the Local Langlands Correspondence.

Citations

• The FPP Conjecture for Real Reductive Groups
• Arithmetic Wavefront Sets and Generic L-packets
• Graded Hecke algebras, constructible sheaves and the p-adic Kazhdan--Lusztig conjecture
• Langlands Classification for L-Parameters
• Rigid inner forms of real and p-adic groups
• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Unitarizable minimal principal series of reductive groups
• Proof of the Tadic conjecture U0 on the unitary dual of GL(m,D)
• Unitary spherical spectrum for split classical groups

Cited by

• Unitary representations attached to parabolic subgroups: the case of abelian unipotent radical

Related

• The FPP Conjecture for Real Reductive Groups
• Vogan’s FPP conjecture for complex Lie groups
• The local Langlands conjecture for the p-adic inner form of Sp(4)
• Deligne-Lusztig constructions for unipotent and p-adic groups
• On depth-zero characters of p-adic groups