TY  - BOOK
AU  - James Arthur 
TI  - The endoscopic classification of representations
T2  - Colloquium Publications
SN  - 978-0-8218-4990-3
AV  - QA179 
PY  - 2013///]
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Mathematics
N1  - 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

N2  - 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. --- summary provioded by publisher
ER  -