The endoscopic classification of representations : orthogonal and symplectic groups
- Arthur, James, 1944- author.
- Providence, Rhode Island : American Mathematical Society, 
- Copyright notice
- Physical description
- xviii, 590 pages ; 26 cm.
- Colloquium publications (American Mathematical Society) ; v. 61.
QA1 .A5225 V.61
- Unknown QA1 .A5225 V.61
- Includes bibliographical references (pages 571-579) and indexes.
- 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)
- 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 L-packets and A-packets), which are parametrised by certain self-dual 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 L-functions, the spectral theory of certain locally symmetric spaces, and to new phenomena for symplectic epsilon-factors. 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 L-functions, 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)
- 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.
- Publication date
- James Arthur.
- Title Variation
- Representations of orthogonal and symplectic groups
- Orthogonal and symplectic groups
- Colloquium publications / American Mathematical Society ; volume 61