تحلیل هارمونیک بر گروه‌های کاهشی و p-ادیک: جلسه ویژه AMS درباره تحلیل هارمونیک و نمایش‌های گروه‌های کاهشی و p-ادیک، ۱۶ ژانویه ۲۰۱۰، سان فرانسیسکو، کالیفرنیا

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. Toward A Mackey Formula For Compact Restriction Of Character Sheaves / Pramod N. Achar And Clifton L.r. Cunningham -- Supercuspidal Characters Of Sl2 Over A P-adic Field / Jeffrey D. Adler [and Others] -- Geometric Structure In The Representation Theory Of Reductive P-adic Groups Ii / Anne-marie Aubert, Paul Baum, And Roger Plymen -- The Construction Of Hecke Algebras Associated To A Coxeter Group / Bill Casselman -- Distinguished Supercuspidal Representations Of Sl2 / Jeffrey Hakim And Joshua M. Lansky -- Twisted Levi Sequences And Explicit Types On Sp4 / Ju-lee Kim And Jiu-kang Yu -- Regularity And Distinction Of Supercuspidal Representations / Fiona Murnaghan -- Patterns In Branching Rules For Irreducible Representations Of Sl2(k), For K A P-adic Field / Monica Nevins -- Parametrizing Nilpotent Orbits In P-adic Symmetric Spaces / Ricardo Portilla -- An Integration Formula Of Shahidi / Steven Spallone -- Managing Metaplectiphobia : Covering P-adic Groups / Martin H. Weissman. Robert S. Doran, Paul J. Sally, Jr., Loren Spice, Editors. Includes Bibliographical References.