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Book DetailsContemporary MathematicsVolume: 543; 2011; 277 ppMSC: Primary 22; 11; 20;
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 HarishChandra'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, MoyPrasad's development of BruhatTits theory relates analysis to group actions on locally finite polysimplicial complexes; the AubertBaumPlymen conjecture relates the local Langlands conjecture to the BaumConnes 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 upperlevel graduate student in representation theory or number theory. The concrete case of the twobytwo special linear group is a constant touchstone.
ReadershipGraduate students and research mathematicians interested in representations of \(p\)adic groups.

Table of Contents

Articles

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 ${\rm SL}_2$ over a $p$adic field [ MR 2798422 ]

AnneMarie Aubert, Paul Baum and Roger Plymen — Geometric structure in the representation theory of reductive $p$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 ${\rm SL}_2$ [ MR 2798425 ]

JuLee Kim and JiuKang Yu — Twisted Levi sequences and explicit types on ${\rm Sp}_4$ [ MR 2798426 ]

Fiona Murnaghan — Regularity and distinction of supercuspidal representations [ MR 2798427 ]

Monica Nevins — Patterns in branching rules for irreducible representations of ${\rm SL}_2(k)$, for $k$ a $p$adic field [ MR 2798428 ]

Ricardo Portilla — Parametrizing nilpotent orbits in $p$adic symmetric spaces [ MR 2798429 ]

Steven Spallone — An integration formula of Shahidi [ MR 2798430 ]

Martin H. Weissman — Managing metaplectiphobia: covering $p$adic groups [ MR 2798431 ]


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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 HarishChandra'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, MoyPrasad's development of BruhatTits theory relates analysis to group actions on locally finite polysimplicial complexes; the AubertBaumPlymen conjecture relates the local Langlands conjecture to the BaumConnes 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 upperlevel graduate student in representation theory or number theory. The concrete case of the twobytwo special linear group is a constant touchstone.
Graduate students and research mathematicians interested in representations of \(p\)adic groups.

Articles

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 ${\rm SL}_2$ over a $p$adic field [ MR 2798422 ]

AnneMarie Aubert, Paul Baum and Roger Plymen — Geometric structure in the representation theory of reductive $p$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 ${\rm SL}_2$ [ MR 2798425 ]

JuLee Kim and JiuKang Yu — Twisted Levi sequences and explicit types on ${\rm Sp}_4$ [ MR 2798426 ]

Fiona Murnaghan — Regularity and distinction of supercuspidal representations [ MR 2798427 ]

Monica Nevins — Patterns in branching rules for irreducible representations of ${\rm SL}_2(k)$, for $k$ a $p$adic field [ MR 2798428 ]

Ricardo Portilla — Parametrizing nilpotent orbits in $p$adic symmetric spaces [ MR 2798429 ]

Steven Spallone — An integration formula of Shahidi [ MR 2798430 ]

Martin H. Weissman — Managing metaplectiphobia: covering $p$adic groups [ MR 2798431 ]