Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Harmonic Analysis on Reductive, $p$-adic Groups
 
Edited by: Robert S. Doran Texas Christian University, Ft. Worth, TX
Paul J. Sally, Jr. University of Chicago, Chicago, IL
Loren Spice Texas Christian University, Ft. Worth, TX
Harmonic Analysis on Reductive, $p$-adic Groups
Softcover ISBN:  978-0-8218-4985-9
Product Code:  CONM/543
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-8222-1
Product Code:  CONM/543.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4985-9
eBook: ISBN:  978-0-8218-8222-1
Product Code:  CONM/543.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Harmonic Analysis on Reductive, $p$-adic Groups
Click above image for expanded view
Harmonic Analysis on Reductive, $p$-adic Groups
Edited by: Robert S. Doran Texas Christian University, Ft. Worth, TX
Paul J. Sally, Jr. University of Chicago, Chicago, IL
Loren Spice Texas Christian University, Ft. Worth, TX
Softcover ISBN:  978-0-8218-4985-9
Product Code:  CONM/543
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-8222-1
Product Code:  CONM/543.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4985-9
eBook ISBN:  978-0-8218-8222-1
Product Code:  CONM/543.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 5432011; 277 pp
    MSC: 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.

    Readership

    Graduate 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 ]
    • 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 ]
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 5432011; 277 pp
MSC: 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.

Readership

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 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.