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Representations of Reductive Groups

In Honor of the 60th Birthday of David A. Vogan, Jr.

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  • © 2015

Overview

Editors:
  1. Monica Nevins

    1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

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    You can also search for this editor in PubMed   Google Scholar

  2. Peter E. Trapa

    1. Dept of Mathematics and Statistics, University of Utah, Salt Lake City, USA

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    You can also search for this editor in PubMed   Google Scholar

  • A unique and comprehensive tribute for David A. Vogan, Jr., a mathematician whose work has had a lasting impact on the field
  • Highlights the depth and breadth of Vogan's influence on representation theory, number theory, automorphic forms, algebraic geometry, and combinatorics
  • Explores many exciting new directions that remain to be explored in the representation theory of reductive groups

Part of the book series: Progress in Mathematics (PM, volume 312)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. The Mathematical Work of David A. Vogan, Jr.

    • William M. McGovern, Peter E. Trapa
    Pages 1-10

  3. On exotic and perverse-coherent sheaves

    • Pramod N. Achar
    Pages 11-49

  4. Parameters for twisted representations

    • Jeffrey Adams, David A. Vogan Jr.
    Pages 51-116

  5. Ladder representations of \(\mathrm{GL}(n, \mathbb{Q}_{p})\)

    • Dan Barbasch, Dan Ciubotaru
    Pages 117-137

  6. Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits

    • Manjul Bhargava, Benedict H. Gross, Xiaoheng Wang
    Pages 139-171

  7. Hecke algebras with unequal parameters and Vogan’s left cell invariants

    • CĂ©dric BonnafĂ©, Meinolf Geck
    Pages 173-187

  8. The smooth loci of spiral Schubert varieties of type \(\widetilde{A}_{2}\)

    • William Graham, Wenjing Li
    Pages 189-226

  9. Centers and cocenters of 0-Hecke algebras

    • Xuhua He
    Pages 227-240

  10. Dirac cohomology, elliptic representations and endoscopy

    • Jing-Song Huang
    Pages 241-276

  11. A program for branching problems in the representation theory of real reductive groups

    • Toshiyuki Kobayashi
    Pages 277-322

  12. Equations for a filtration of sheets and the variety of singular elements of a complex semisimple Lie algebra

    • Bertram Kostant
    Pages 323-332

  13. On conjugacy classes in a reductive group

    • George Lusztig
    Pages 333-363

  14. Hecke algebras and involutions in Coxeter groups

    • George Lusztig, David A. Vogan Jr.
    Pages 365-398

  15. Comparing and characterizing some constructions of canonical bases from Coxeter systems

    • Eric Marberg
    Pages 399-436

  16. Upper semicontinuity of KLV polynomials for certain blocks of Harish-Chandra modules

    • William M. McGovern
    Pages 437-441

  17. Hodge theory and unitary representations

    • Wilfried Schmid, Kari Vilonen
    Pages 443-453

  18. On elliptic factors in real endoscopic transfer I

    • Diana Shelstad
    Pages 455-504

  19. On the Gelfand–Kirillov dimension of a discrete series representation

    • Nolan R. Wallach
    Pages 505-516

  20. A reducible characteristic variety in type A

    • Geordie Williamson
    Pages 517-532
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Keywords

About this book

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups.  His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics.

Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014.  This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored.  Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context.

Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Editors and Affiliations

  • Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Monica Nevins

  • Dept of Mathematics and Statistics, University of Utah, Salt Lake City, USA

    Peter E. Trapa

Bibliographic Information

  • Book Title: Representations of Reductive Groups

  • Book Subtitle: In Honor of the 60th Birthday of David A. Vogan, Jr.

  • Editors: Monica Nevins, Peter E. Trapa

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-23443-4

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-23442-7Published: 06 January 2016

  • Softcover ISBN: 978-3-319-79483-9Published: 30 March 2018

  • eBook ISBN: 978-3-319-23443-4Published: 18 December 2015

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XIX, 532

  • Number of Illustrations: 1 b/w illustrations, 6 illustrations in colour

  • Topics: Topological Groups, Lie Groups, Algebraic Geometry, Number Theory

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