Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms

This volume presents a panorama of the diverse activities organized by V. Heiermann and D. Prasad in Marseille at the CIRM for the Chaire Morlet event during the first semester of 2016. It assembles together expository articles on topics which previously could only be found in research papers. Starting with a very detailed article by P. Baumann and S. Riche on the geometric Satake correspondence, the book continues with three introductory articles on distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen; an expository article of I. Badulescu on the JacquetLanglands correspondence; a paper of J. Arthur on functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the Simons Proceedings; an article of W-W. Li attempting to generalize GodementJacquet theory; and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local Langlands classification for classical groups. The book should be of interest to students as well as professional researchers working in the broad area of number theory and representation theory.

Based on a workshop and a conference at CIRM in Luminy in 2016 attended by both graduate students and very senior practitioners of the subject. Features several excellent review articles which can be read by students entering research in many areas of number theory. Includes several high level research articles. Begins with an article on the geometric Satake isomorphism, a key theorem in the geometric Langlands program.

Autorentext
Volker Heiermann is a Professor of Mathematics at the Aix Marseille Université, Luminy.
Dipendra Prasad is a Professor of Mathematics at the Tata Institute of Fundamental Research, Mumbai.
The authors are established researchers in the broad subject of Automorphic forms who came together at CIRM Luminy during the first half of 2016 on Chaire Morlet,a distinguished research Chaire created by the CIRM, Aix Marseille University, the city of Marseille.

Inhalt

• Notes on the Geometric Satake Equivalence. - Distinguished Representations of Reductive p -Adic Groups. - Period Integrals of Automorphic Forms and Local Distinction. - The Trace Formula and the Proof of the Global Jacquet-Langlands Correspondence. - Distinction of Representations via Bruhat-Tits Buildings of p -Adic Groups. - Towards Generalized Prehomogeneous Zeta Integrals. - Functoriality and the Trace Formula. - Sur les paquets d'Arthur des groupes classiques et unitaires non quasi-déployés.