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- DescriptionWithin the Langlands programme, endoscopy is a fundamental process for relating automorphic representations of one group with those of ather. 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 (kwn 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 phemena 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.
- Author BiographyJames Arthur, University of Toronto, ON, Canada.
- Author(s)James Arthur
- PublisherAmerican Mathematical Society
- Date of Publication30/11/2013
- Series TitleColloquium Publications
- Series Part/Volume Number61
- Place of PublicationProvidence
- Country of PublicationUnited States
- ImprintAmerican Mathematical Society
- Content Noteillustrations
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