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
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-Chandr...
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| Hauptverfasser: | , , , |
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| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, R.I
American Mathematical Society
2011
|
| Schriftenreihe: | Contemporary mathematics |
| Schlagworte: |
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
|
| ISBN: | 0821849859, 9780821849859 |
| Online-Zugang: | Volltext |
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| Abstract | 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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| AbstractList | 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. |
| Author | Sally, Paul Doran, Robert S. Spice, Loren AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Groups |
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| Notes | Includes bibliographical references and index |
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| SubjectTerms | 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 |
| Title | 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 |
| URI | https://cir.nii.ac.jp/crid/1130282270102710912 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9780821882221&uid=none |
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