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

• Main Authors: AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Groups, Doran, Robert S., Sally, Paul, Spice, Loren
• Format: eBook Book
• Language: English
• Published: Providence, R.I American Mathematical Society 2011
• Series: Contemporary mathematics
• Subjects: Group theory and generalizations > Linear algebraic groups and related topics > Linear algebraic groups over finite fields. msc; Group theory and generalizations > Linear algebraic groups and related topics > Linear algebraic groups over local fields and their integers. msc; Group theory and generalizations > Linear algebraic groups and related topics > Representation theory. msc; Group theory and generalizations > Representation theory of groups > Representations of finite groups of Lie type. msc; Harmonic analysis; Harmonic analysis > Congresses; Number theory > Discontinuous groups and automorphic forms > Representation-theoretic methods; automorphic representations over local and global fields. msc; p-adic groups; p-adic groups > Congresses; Representations of Lie groups; Representations of Lie groups > Congresses; Topological groups, Lie groups > Lie groups > Analysis on $p$-adic Lie groups. msc; Topological groups, Lie groups > Lie groups > Representations of Lie and linear algebraic groups over local fields. msc
• ISBN: 0821849859; 9780821849859

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.