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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 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.
ReadershipGraduate students and research mathematicians interested in representations of \(p\)-adic groups.
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Table of Contents
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Articles
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Pramod N. Achar and Clifton L. R. Cunningham — Toward a Mackey formula for compact restriction of character sheaves [ MR 2798421 ]
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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 ]
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Anne-Marie Aubert, Paul Baum and Roger Plymen — Geometric structure in the representation theory of reductive $p$-adic groups II [ MR 2798423 ]
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Bill Casselman — The construction of Hecke algebras associated to a Coxeter group [ MR 2798424 ]
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Jeffrey Hakim and Joshua M. Lansky — Distinguished supercuspidal representations of ${\rm SL}_2$ [ MR 2798425 ]
-
Ju-Lee Kim and Jiu-Kang Yu — Twisted Levi sequences and explicit types on ${\rm Sp}_4$ [ MR 2798426 ]
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Fiona Murnaghan — Regularity and distinction of supercuspidal representations [ MR 2798427 ]
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Monica Nevins — Patterns in branching rules for irreducible representations of ${\rm SL}_2(k)$, for $k$ a $p$-adic field [ MR 2798428 ]
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Ricardo Portilla — Parametrizing nilpotent orbits in $p$-adic symmetric spaces [ MR 2798429 ]
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Steven Spallone — An integration formula of Shahidi [ MR 2798430 ]
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Martin H. Weissman — Managing metaplectiphobia: covering $p$-adic groups [ MR 2798431 ]
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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.
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 ]
-
Anne-Marie 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 ]
-
Ju-Lee Kim and Jiu-Kang 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 ]
