The FPP Conjecture for p-adic Groups

Dihua Jiang; Baiying Liu; Chi-Heng Lo; Lucas Mason-Brown

paper

The FPP Conjecture for p-adic Groups

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.