bigcovers/noimage.jpg
The Endoscopic Classification of Representations
James Arthur
Price
2200.00
ISBN
9781470438371
Language
English
Pages
612
Format
Paperback
Dimensions
158 x 240 mm
Year of Publishing
2017
Territorial Rights
Restricted
Imprint
Universities Press
Catalogues

Within the Langlands program, 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 parametrized 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 program.

The methods are by comparison of the trace formula of G with its stabilization (and a comparison of the twisted trace formula of GL(N) with its stabilization, 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 program.

James Arthur: University of Toronto, Toronto, ON, Canada

THE BOOKPOINT (INDIA) PVT. LTD.
3-6-752 Himayatnagar, Hyderabad,
500 029 Telangana
Phone: (040) 27662849, 27662850
Email: info@thebookpointindia.com
Copyright © The Bookpoint (India) Pvt. Ltd. All rights reserved.
Disclaimer and Privacy Policy
Terms and Conditions
Frequently Asked Questions