Un caractère relatif pondéré

2025/12/18 by Pierre-Henri Chaudouard, Chaudouard, Pierre-Henri
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.2512.17056

Abstract

Let p≥ 1. The symmetric space S=GL(2p+1)/GL(p+1)× GL(p) (over a number field) is not cuspidal in the sense that its automorphic spectrum does not contain any cuspidal representation of GL(2p+1). In this article, we compute the spectral decomposition of its relatively cuspidal part: this is, by definition, the part of the spectrum that is induced from the cuspidal part of the symmetric space (GL(1)× GL(2p)) / (GL(1)× GL(p)× GL(p)). As an application, we obtain the expression of the contribution of this relatively cuspidal part to the Guo-Jacquet trace formula (established by H. Li and the author) in terms of a weighted relative character.

Citations

• Intertwining periods, L-functions and local-global principles for distinction of automorphic representations
• On dual groups of symmetric varieties and distinguished representations of p-adic groups
• The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case
• On linear periods
• Periods and harmonic analysis on spherical varieties
• Spherical functions on spherical varieties

Related

• Isolation of the Cuspidal Spectrum: the Function Field Case
• Cuspidality criterion for symmetric powers of automorphic representations of GL(2) over function fields
• Isolation of cuspidal spectrum, with application to the Gan--Gross--Prasad conjecture
• A spectral expansion for the symmetric space GL_n(E)/GL_n(F)
• Relative Trace Formula And Simultaneous Nonvanishing for GL₃ x GL₂ and GL₃ x GL₁ L-functions