2008/03/24 by Avraham Aizenbud, Aizenbud, Avraham, Dmitry Gourevitch +3 · 2 citations
Mathematics · #14L24 #14L30 #20C99 #20G05 #20G25 #22E45 #46F10 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14L24 #msc:14L30 #msc:20C99 #msc:20G05 #msc:20G25 #msc:22E45 #msc:46F10
paper · pdf · doi:10.48550/arxiv.0803.3395
34 pages, 1 figure. v2: A proof of a version of localization principle inserted. v3: minor changes. v4: definition of symmetric pair slightly changed. v5: minor changes + lemma D.0.3 added for clarification. v6: minor changes - see Theorem 4.0.5. v7:minor changes. Appendix A by Avraham Aizenbud, Dmitry Gourevitch and Eitan Sayag
openalex publication_date 2008/03/24 · arxiv created 2009/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of the paper we generalize a descent technique due to Harish-Chandra to the case of a reductive group acting on a smooth affine variety both defined over arbitrary local field F of characteristic zero. Our main tool is Luna slice theorem. In the second part of the paper we apply this technique to symmetric pairs. In particular we prove that the pair (GL(n,C),GL(n,R)) is a Gelfand pair. We also prove that any conjugation invariant distribution on GL(n,F) is invariant with respect to transposition. For non-archimedean F the later is a classical theorem of Gelfand and Kazhdan. We use the techniques developed here in our subsequent work [AG3] where we prove an archimedean analog of the theorem on uniqueness of linear periods by H. Jacquet and S. Rallis.