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Hardcover ISBN:  9780821849903 
Product Code:  COLL/61 
List Price:  $115.00 
MAA Member Price:  $103.50 
AMS Member Price:  $92.00 
eBook ISBN:  9781470409692 
Product Code:  COLL/61.E 
List Price:  $115.00 
MAA Member Price:  $103.50 
AMS Member Price:  $92.00 
Hardcover ISBN:  9780821849903 
eBookISBN:  9781470409692 
Product Code:  COLL/61.B 
List Price:  $230.00$172.50 
MAA Member Price:  $207.00$155.25 
AMS Member Price:  $184.00$138.00 

Book DetailsColloquium PublicationsVolume: 61; 2013; 590 ppMSC: Primary 22; 11; 58;
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 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 \(L\)functions, 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 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.ReadershipResearch mathematicians interested in automorphic forms, the Langlands program, and number theory.

Table of Contents

Chapters

Chapter 1. Parameters

Chapter 2. Local transfer

Chapter 3. Global stabilization

Chapter 4. The standard model

Chapter 5. A study of critical cases

Chapter 6. The local classification

Chapter 7. Local nontempered representations

Chapter 8. The global classification

Chapter 9. Inner forms


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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 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 \(L\)functions, 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 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.
Research mathematicians interested in automorphic forms, the Langlands program, and number theory.

Chapters

Chapter 1. Parameters

Chapter 2. Local transfer

Chapter 3. Global stabilization

Chapter 4. The standard model

Chapter 5. A study of critical cases

Chapter 6. The local classification

Chapter 7. Local nontempered representations

Chapter 8. The global classification

Chapter 9. Inner forms