A spectral decomposition of orbital integrals for PGL(2,F)

2017/01/18 by David Kazhdan, Kazhdan, David, Stephen DeBacker +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1701.04999

Abstract

Let F be a local non-archimedian field, G a semisimple F-group, dg a Haar measure on G and \mathcal S(G) be the space of locally constant complex valued functions f on G with compact support. For any regular elliptic congugacy class Ω=h^G⊂ G we denote by I_Ω the G-invariant functional on \mathcal S (G) given by I_Ω(f)=∫_G f(g^-1hg)dg This paper provides the spectral decomposition of functionals I_Ω in the case G=PGL(2,F) and in the last section first steps of such an analysis for the general case.

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