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Vertex Operators in Mathematics and Physics

Proceedings of a Conference November 10–17, 1983

  • Conference proceedings
  • © 1985

Overview

Editors:
  1. J. Lepowsky

    1. Department of Mathematics, Rutgers University, New Brunswick, USA

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  2. S. Mandelstam

    1. Department of Physics, University of California, Berkeley, USA

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  3. I. M. Singer

    1. Department of Mathematics, University of California, Berkeley, USA
      Mathematical Sciences Research Institute, Berkeley, USA

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

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Table of contents (23 papers)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    1. Introduction

      • James Lepowsky
      Pages 1-13

  3. String models

    1. Introduction to String Models and Vertex Operators

      • S. Mandelstam
      Pages 15-35

    2. An Introduction to Polyakov’s String Model

      • Orlando Alvarez
      Pages 37-47

    3. Conformally Invariant Field Theories in Two Dimensions

      • Thomas Curtright
      Pages 49-50

  4. Lie algebra representations

    1. Algebras, Lattices and Strings

      • P. Goddard, D. Olive
      Pages 51-96

    2. Z-Algebras and the Rogers-Ramanujan Identities

      • James Lepowsky, Robert Lee Wilson
      Pages 97-142

    3. Structure of the Standard Modules for the Affine Lie Algebra A1 (1) in the Homogeneous Picture

      • J. Lepowsky, M. Primc
      Pages 143-162

    4. Standard Representations of Some Affine Lie Algebras

      • Kailash C. Misra
      Pages 163-183

    5. Some Applications of Vertex Operators to Kac-Moody Algebras

      • Alex J. Feingold
      Pages 185-206

    6. On a Duality of Branching Coefficients

      • Michio Jimbo, Tetsuji Miwa
      Pages 207-216

  5. The Monster

    1. A Brief Introduction to the Finite Simple Groups

      • Robert L. Griess Jr.
      Pages 217-229

    2. A Moonshine Module for the Monster

      • Igor B. Frenkel, James Lepowsky, Arne Meurman
      Pages 231-273
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    J. Lepowsky

  • Department of Physics, University of California, Berkeley, USA

    S. Mandelstam

  • Department of Mathematics, University of California, Berkeley, USA

    I. M. Singer

  • Mathematical Sciences Research Institute, Berkeley, USA

    I. M. Singer

Bibliographic Information

  • Book Title: Vertex Operators in Mathematics and Physics

  • Book Subtitle: Proceedings of a Conference November 10–17, 1983

  • Editors: J. Lepowsky, S. Mandelstam, I. M. Singer

  • Series Title: Mathematical Sciences Research Institute Publications

  • DOI: https://doi.org/10.1007/978-1-4613-9550-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1985

  • Softcover ISBN: 978-1-4613-9552-2Published: 12 April 2013

  • eBook ISBN: 978-1-4613-9550-8Published: 08 March 2013

  • Series ISSN: 0940-4740

  • Edition Number: 1

  • Number of Pages: XIV, 482

  • Topics: Theoretical, Mathematical and Computational Physics

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