Harmonic Analysis on Reductive, $p$-adic Groups

Harmonic Analysis on Reductive, $p$-adic Groups

by Robert S. Doran, Paul Sally
     
 

ISBN-10: 0821849859

ISBN-13: 9780821849859

Pub. Date: 05/26/2011

Publisher: American Mathematical Society

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

Overview

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.

Product Details

ISBN-13:
9780821849859
Publisher:
American Mathematical Society
Publication date:
05/26/2011
Series:
Contemporary Mathematics Series, #543
Pages:
277
Product dimensions:
7.00(w) x 10.00(h) x 0.50(d)

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