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.
About James Arthur
James Arthur, University of Toronto, ON, Canada.Details Book
Author  :  James Arthur 
Publisher  :  American Mathematical Society 
Data Published  :  30 October 2013 
ISBN  :  0821849905 
EAN  :  9780821849903 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  595 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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