A relative trace formula identity for non-tempered spherical varieties

2025/12/03 by Wan, Chen
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.03320

Abstract

In this paper, motivated by some previous works in residue method and the recent theory of the relative Langlands duality, we prove a relative trace formula identity that compares the period integral of non-tempered spherical varieties with the period integral of a tempered spherical varieties associated to a Levi subgroup. This allows us to incorporate numerous relative trace formula comparisons studied during the last four decades under the relative Langlands duality framework. We will also propose a conjectural comparison for general non-tempered Hamiltonian spaces.

Citations

• Relative Langlands Duality
• Strongly tempered hyperspherical Hamiltonian spaces
• On the residue method for period integrals
• Generic representations for symmetric spaces
• Periods and harmonic analysis on spherical varieties
• The spherical systems of the wonderful reductive subgroups

Related

• BZSV Duality for Some Strongly Tempered Spherical Varieties
• Beyond endoscopy for the relative trace formula I: local theory
• Relative functoriality and functional equations via trace formulas
• Spherical varieties and integral representations of L-functions
• Introduction to the relative Langlands program