Endoscopic Relative Orbital Integrals on U₃

2021/10/22 by Chung-Ru Lee, Lee, Chung-Ru
Mathematics · #11F66 #11F70 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2110.11890

openalex publication_date 2021/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a nonarchimedean local field and consider the action of the reductive group SO₃(F) on the spherical variety (U₃/O₃)(F). We compute the endoscopic orbital integrals of the basic function in this situation. Knowing the endoscopic orbital integrals is essential for observing the existence of transfer in this relative setting. This would be the first time such a computation has appeared in the literature for spherical varieties with type N-spherical roots.

Related

• Endoscopic transfer of orbital integrals in large residual characteristic
• Computations of orbital integrals and Shalika germs
• Exposing Relative Endoscopy in Unitary Symmetric Spaces
• An explicit formula for the orbital integrals on the spherical Hecke algebra of GL₃
• Spherical character of a supercuspidal representation as weighted orbital integral