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 / Robert S. Doran, Paul J. Sally, Jr., Loren Spice, editors.

Format:

• Book
• Conference/Event

Contributor:

• Doran, Robert S., 1937- editor.
• Sally, Paul J., Jr., 1933-2013, editor.
• Spice, Loren, 1981- editor.

Conference Name:

• AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Groups (2010 : San Francisco, Calif.), issuing body.
• AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Groups

Series:

• Contemporary mathematics, 0271-4132 543
• Contemporary mathematics, 543 0271-4132

Language:

English

Subjects (All):

• Representations of Lie groups--Congresses.
• p-adic groups--Congresses.
• Harmonic analysis--Congresses.

Physical Description:

1 online resource (294 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2011]

Language Note:

English

Summary:

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.

Contents:

• Contents
• Preface
• List of Participants
• Toward a Mackey formula for compact restriction of character sheaves
• Supercuspidal characters of SL2 over a p-adic field
• 1. Introduction
• 2. Field extensions
• 3. Tori
• 4. A principal-value integral
• 5. The building and filtrations
• 6. Haar measure
• 7. Duality, Fourier transforms, and orbital integrals
• 8. Unrefined minimal K-types
• 9. Representations of depth zero
• 10. Representations of positive depth
• 11. Parametrization of supercuspidal representations
• 12. Inducing representations
• 13. Murnaghan-Kirillov theory
• 14. "Ordinary" supercuspidal characters
• 15. "Exceptional" supercuspidal characters
• References
• Geometric structure in the representation theory of reductive p-adic groups II
• The construction of Hecke algebras associated to a Coxeter group
• 1. The Hecke algebras of finite reductive groups
• 2. Coxeter groups
• 3. The Hecke algebra of a Coxeter group
• 4. Generators and relations
• 5. References
• Distinguished supercuspidal representations of SL2
• 2. Elliptic tori
• 3. Involutions of SL2
• 4. Multiplicity constants
• 5. Supercuspidal representations
• 6. Distinguished toral supercuspidal representations
• 7. Distinguished depth-zero supercuspidal representations
• Appendix A. The building and the Moy-Prasad groups
• Twisted Levi sequences and explicit types on Sp4
• Regularity and distinction of supercuspidal representations
• Patterns in branching rules for irreducible representations of SL2(k), for k a p-adic field
• Parametrizing nilpotent orbits in p-adic symmetric spaces
• An integration formula of Shahidi
• Managing metaplectiphobia: Covering p-adic groups.

Notes:

• Description based upon print version of record.
• Includes bibliographical references.
• Description based on print version record.

ISBN:

0-8218-8222-8