Vertex Operators in Mathematics and Physics

Proceedings of a Conference November 10–17, 1983

  • J. Lepowsky
  • S. Mandelstam
  • I. M. Singer

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 3)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. James Lepowsky
      Pages 1-13
  3. String models

  4. Lie algebra representations

    1. P. Goddard, D. Olive
      Pages 51-96
    2. James Lepowsky, Robert Lee Wilson
      Pages 97-142
    3. Michio Jimbo, Tetsuji Miwa
      Pages 207-216
  5. The Monster

    1. Robert L. Griess Jr.
      Pages 217-229
    2. Igor B. Frenkel, James Lepowsky, Arne Meurman
      Pages 231-273
  6. Integrable Systems

About these proceedings


James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.


Lie algebra Operator (Math.) Operators Physics Scheitel (Math.)

Editors and affiliations

  • J. Lepowsky
    • 1
  • S. Mandelstam
    • 2
  • I. M. Singer
    • 3
    • 4
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Department of PhysicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  4. 4.Mathematical Sciences Research InstituteBerkeleyUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9552-2
  • Online ISBN 978-1-4613-9550-8
  • Series Print ISSN 0940-4740
  • About this book