Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms

Volker Heiermann (1) , Dipendra Prasad (2)

1 I2M - Institut de Mathématiques de Marseille
2 TIFR - Tata Institute for Fundamental Research

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 Jacquet–Langlands 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 Godement–Jacquet 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.

Mots clés: geometric Satake correspondence; Jacquet–Langlands correspondence; functoriality; trace formula; Godement–Jacquet theory; representation theory; number theory; geometric Langlands program; geometric Satake isomorphism

Domaines: Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Volker Heiermann, Dipendra Prasad. Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms: CIRM Jean-Morlet Chair, Spring 2016. Volker Heiermann; Dipendra Prasad. Springer International Publishing, 2221, pp.vii+361, 2018, Lecture Notes in Mathematics, 978-3-319-95231-4. ⟨10.1007/978-3-319-95231-4⟩. ⟨hal-02064687⟩