Non-Abelian Harmonic Analysis

Applications of SL (2,ℝ)

  • Roger Howe
  • Eng Chye Tan

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Roger Howe, Eng Chye Tan
    Pages 1-50
  3. Roger Howe, Eng Chye Tan
    Pages 51-92
  4. Roger Howe, Eng Chye Tan
    Pages 93-120
  5. Roger Howe, Eng Chye Tan
    Pages 121-202
  6. Roger Howe, Eng Chye Tan
    Pages 203-242
  7. Back Matter
    Pages 243-259

About this book

Introduction

This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ­ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it­ self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin­ ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom­ ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.

Keywords

Fourier analysis Lie Matrix algebra classification eigenvector equation ergodic theory group lie algebra presentation representation theory symmetric relation themes theorem

Editors and affiliations

  • Roger Howe
    • 1
  • Eng Chye Tan
    • 2
  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.Department of MathematicsNational University of SingaporeSingapore

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9200-2
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-97768-3
  • Online ISBN 978-1-4613-9200-2
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book