Harmonic analysis on reductive, p-adic groups : AMS special session on harmonic analysis and representations of reductive, p-adic groups, January 16, 2010, San Francisco, CA

書誌事項

Harmonic analysis on reductive, p-adic groups : AMS special session on harmonic analysis and representations of reductive, p-adic groups, January 16, 2010, San Francisco, CA

Robert S. Doran, Paul J. Sally, Jr., Loren Spice, editors

(Contemporary mathematics, 543)

American Mathematical Society, c2011

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

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