Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences

2012/12/28 by Dihua Jiang, Jiang, Dihua
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Finite Group Theory Research #math.RT #msc:11F70 #msc:11F85 #msc:22E50 #msc:22E55

paper · pdf · doi:10.48550/arxiv.1212.6525

80 pages, submitted to the proceedings of the conference: Automorphic Forms and Related Geometry: assessing the legacy of I.I. Piatetski-Shapiro

arxiv created 2012/12/28 · arxiv updated 2013/01/01

Abstract

A general framework of constructions of endoscopy correspondences via automorphic integral transforms for classical groups is formulated in terms of the Arthur classification of the discrete spectrum of square-integrable automorphic forms. This suggests a principle, which is called the (τ,b)-theory of automorphic forms of classical groups, to reorganize and extend the series of work of Piatetski-Shapiro, Rallis, Kudla and others on standard L-functions of classical groups and theta correspondence.

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