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New Developments in Lie Theory and Their Applications

  • Book
  • © 1992

Overview

Editors:
  1. Juan Tirao

    1. Facultad de Matematica Astronomia y Fisica, Universidad Nacional de Córdoba, Córdoba, Argentina

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  2. Nolan R. Wallach

    1. Dept. of Mathematics, University of California at San Diego, La Jolla, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Mathematics (PM, volume 105)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-ix
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  2. Automorphic Forms

    • Nolan R. Wallach
    Pages 1-25

  3. Analytic and Geometric Realization of Representations

    • Wilfried Schmid
    Pages 27-47

  4. Introduction to Quantized Enveloping Algebras

    • George Lusztig
    Pages 49-65

  5. The Vanishing of Scalar Curvature on 6 Manifolds, Einstein’s Equation, and Representation Theory

    • Bertram Kostant
    Pages 67-86

  6. Unitary Representations of Reductive Lie Groups and the Orbit Method

    • David A. Vogan Jr.
    Pages 87-114

  7. Twistor Theory for Riemannian Manifolds

    • John Rawnsley
    Pages 115-128

  8. You Can’t Hear the Shape of a Manifold

    • Carolyn S. Gordon
    Pages 129-146

  9. Kuznetsov Formulas

    • R. J. Miatello
    Pages 147-154

  10. Lefschetz Numbers and Cyclic Base Change for Purely Imaginary Extensions

    • Jurgen Rohlfs, Birgit Speh
    Pages 155-161

  11. Some Zeta Functions Attached to Γ\G/K

    • Floyd L. Williams
    Pages 163-177

  12. On the Centralizer of K in the Universal Enveloping Algebra of SO(n, 1) and SU(n, 1)

    • Juan A. Tirao
    Pages 179-186

  13. On Spherical Modules

    • Nicolás Andruskiewitsch
    Pages 187-198

  14. Generalized Weil Representations for SL(n,k), n odd, k a Finite Field

    • José Pantoja, Jorge Soto-Andrade
    Pages 199-206

  15. Local Multiplicity of the Intersection of Lagrangian Cycles and the Index of Holonomic Modules

    • Alberto S. Dubson
    Pages 207-225

  16. Back Matter

    Pages 227-228
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Keywords

About this book

Representation theory, and more generally Lie theory, has played a very important role in many of the recent developments of mathematics and in the interaction of mathematics with physics. In August-September 1989, a workshop (Third Workshop on Representation Theory of Lie Groups and its Applications) was held in the environs of C6rdoba, Argentina to present expositions of important recent developments in the field that would be accessible to graduate students and researchers in related fields. This volume contains articles that are edited versions of the lectures (and short courses) given at the workshop. Within representation theory, one of the main open problems is to determine the unitary dual of a real reductive group. Although this prob­ lem is as yet unsolved, the recent work of Barbasch, Vogan, Arthur as well as others has shed new light on the structure of the problem. The article of D. Vogan presents an exposition of some aspects of this prob­ lem, emphasizing an extension of the orbit method of Kostant, Kirillov. Several examples are given that explain why the orbit method should be extended and how this extension should be implemented.

Editors and Affiliations

  • Facultad de Matematica Astronomia y Fisica, Universidad Nacional de Córdoba, Córdoba, Argentina

    Juan Tirao

  • Dept. of Mathematics, University of California at San Diego, La Jolla, USA

    Nolan R. Wallach

Bibliographic Information

  • Book Title: New Developments in Lie Theory and Their Applications

  • Editors: Juan Tirao, Nolan R. Wallach

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-2978-0

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1992

  • Hardcover ISBN: 978-0-8176-3619-7Due: 01 October 1992

  • Softcover ISBN: 978-1-4612-7743-9Published: 26 September 2011

  • eBook ISBN: 978-1-4612-2978-0Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: X, 228

  • Topics: Topological Groups, Lie Groups, Group Theory and Generalizations

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