Automorphic Representation of Unitary Groups in Three Variables. (AM-123), Volume 123 (Annals of Mathematics Studies)

The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups. Table of Contents Introduction 1. Preliminary definitions and notation 2. The trace formula 3. Stable conjugacy 4. Orbital integrals and endoscopic groups 5. Stabilization 6. Weighted orbital integrals 7. Elliptic singular terms 8. Germ expansions and limit formulas 9. Singularities 10. The stable trace formula 11. The unitary group in two variables 12. Representation theory 13. Automorphic representations 14. Comparison of inner forms 15. Additional results References Subject Index Notation Index