The endoscopic classification of representations : orthogonal and symplectic groups
 Responsibility
 James Arthur.
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2013]
 Copyright notice
 ©2013.
 Physical description
 xviii, 590 pages ; 26 cm.
 Series
 Colloquium publications (American Mathematical Society) ; v. 61.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA1 .A5225 V.61  Unknown 
More options
Creators/Contributors
 Author/Creator
 Arthur, James, 1944 author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 571579) and indexes.
 Contents

 Table of Contents:* Parameters * Local transfer * Global stabilization * The standard model * A study of critical cases * The local classification * Local nontempered representations * The global classification * Inner forms * Bibliography * Index.
 (source: Nielsen Book Data)9780821849903 20160612
 Publisher's Summary
 Within the Langlands programme, endoscopy is a fundamental process for relating automorphic representations of one group with those of another. In this book, Arthur establishes an endoscopic classification of automorphic representations of orthogonal and symplectic groups G. The representations are shown to occur in families (known as global Lpackets and Apackets), which are parametrised by certain selfdual automorphic representations of an associated general linear group GL(N). The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of G for any representation in a family. The results of the volume have already had significant applications: to the local Langlands correspondence, the construction of unitary representations, the existence of Whittaker models, the analytic behaviour of Langlands Lfunctions, the spectral theory of certain locally symmetric spaces, and to new phenomena for symplectic epsilonfactors. One can expect many more. In fact, it is likely that both the results and the techniques of the volume will have applications to almost all sides of the Langlands programme. The methods are by comparison of the trace formula of G with its stabilisation (and a comparison of the twisted trace formula of $GL(N) with its stabilisation, which is part of work in progress by Moeglin and Waldspurger). This approach is quite different from methods that are based on Lfunctions, converse theorems, or the theta correspondence. The comparison of trace formulas in the volume ought to be applicable to a much larger class of groups. Any extension at all will have further important implications for the Langlands programme.
(source: Nielsen Book Data)9780821849903 20160612
Subjects
 Subject
 Representations of groups.
 Linear algebraic groups.
 Class field theory.
 Algebraic number theory.
 Topological groups, Lie groups > Lie groups > Representations of Lie and linear algebraic groups over global fields and adèle rings.
 Topological groups, Lie groups > Lie groups > Representations of Lie and linear algebraic groups over local fields.
 Number theory > Algebraic number theory: global fields > Class field theory.
 Number theory > Discontinuous groups and automorphic forms > Langlands $L$functions; one variable Dirichlet series and functional equations.
 Global analysis, analysis on manifolds > Calculus on manifolds; nonlinear operators > Spectral theory; eigenvalue problems.
Bibliographic information
 Publication date
 2013
 Title Variation
 Representations of orthogonal and symplectic groups
 Orthogonal and symplectic groups
 Series
 Colloquium publications / American Mathematical Society ; volume 61
 ISBN
 9780821849903 (alk. paper)
 0821849905 (alk. paper)