Harmonic Analysis on Reductive, -adic Groups
About this Title
Robert S. Doran, Paul J. Sally, Jr. and Loren Spice, Editors
Publication: Contemporary Mathematics
Publication Year : Volume 543
ISBNs: 978-0-8218-4985-9 (print); 978-0-8218-8222-1 (online)
MathSciNet review: 2797388
This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Representations of Reductive, $p$-adic Groups, which was held on January 16, 2010, in San Francisco, California.
One of the original guiding philosophies of harmonic analysis on $p$-adic groups was Harish-Chandra's Lefschetz principle, which suggested a strong analogy with real groups. From this beginning, the subject has developed a surprising variety of tools and applications. To mention just a few, Moy-Prasad's development of Bruhat-Tits theory relates analysis to group actions on locally finite polysimplicial complexes; the Aubert-Baum-Plymen conjecture relates the local Langlands conjecture to the Baum-Connes conjecture via a geometric description of the Bernstein spectrum; the $p$-adic analogues of classical symmetric spaces play an essential role in classifying representations; and character sheaves, originally developed by Lusztig in the context of finite groups of Lie type, also have connections to characters of $p$-adic groups.
The papers in this volume present both expository and research articles on these and related topics, presenting a broad picture of the current state of the art in $p$-adic harmonic analysis. The concepts are liberally illustrated with examples, usually appropriate for an upper-level graduate student in representation theory or number theory. The concrete case of the two-by-two special linear group is a constant touchstone.
Graduate students and research mathematicians interested in representations of $p$-adic groups.
Table of Contents
- Pramod N. Achar and Clifton L. R. Cunningham – Toward a Mackey formula for compact restriction of character sheaves [MR 2798421]
- Jeffrey D. Adler, Stephen DeBacker, Paul J. Sally, Jr. and Loren Spice – Supercuspidal characters of over a -adic field [MR 2798422]
- Anne-Marie Aubert, Paul Baum and Roger Plymen – Geometric structure in the representation theory of reductive -adic groups II [MR 2798423]
- Bill Casselman – The construction of Hecke algebras associated to a Coxeter group [MR 2798424]
- Jeffrey Hakim and Joshua M. Lansky – Distinguished supercuspidal representations of [MR 2798425]
- Ju-Lee Kim and Jiu-Kang Yu – Twisted Levi sequences and explicit types on [MR 2798426]
- Fiona Murnaghan – Regularity and distinction of supercuspidal representations [MR 2798427]
- Monica Nevins – Patterns in branching rules for irreducible representations of , for a -adic field [MR 2798428]
- Ricardo Portilla – Parametrizing nilpotent orbits in -adic symmetric spaces [MR 2798429]
- Steven Spallone – An integration formula of Shahidi [MR 2798430]
- Martin H. Weissman – Managing metaplectiphobia: covering -adic groups [MR 2798431]