Categories of symmetries and infinite-dimensional groups

Author(s)

Bibliographic Information

Categories of symmetries and infinite-dimensional groups

Yu.A. Neretin ; translated [from the Russian] by G.G. Gould

(London Mathematical Society monographs, new ser., 16)

Clarendon Press , Oxford University Press, 1996

Available at  / 31 libraries

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Includes bibliographical references and index

Description and Table of Contents

Description

For mathematicians working in group theory, the study of the many infinite-dimensional groups has been carried out in an individual and non-coherent way. For the first time, these apparently disparate groups have been placed together, in order to construct the `big picture'. This book successfully gives an account of this - and shows how such seemingly dissimilar types such as the various groups of operators on Hilbert spaces, or current groups are shown to belong to a bigger entitity. This is a ground-breaking text will be important reading for advanced undergraduate and graduate mathematicians.

Table of Contents

  • Preface
  • 1. Visible and invisible structures on infinite-dimensional groups
  • 2. Spinor representation
  • 3. Representations of the complex classical categories
  • 4. Fermion Fock space
  • 5. The Weil representation: finite-dimensional case
  • 6. The Weil representation: infinite-dimensional case
  • 7. Representations of the diffeomorphisms of a circle and the Virasoro algebra
  • 8. The heavy groups
  • 9. Infinite-dimensional classical groups and almost invariant structures
  • 10. Some algebraic constructions of measure theory
  • Appendix A The real classical categories
  • Appendix B Semple complexes, hinges, and boundaries of symmetric spaces
  • Appendix C Boson-fermion correspondence
  • Appendix D Univalent functions and the Grunsky operator
  • Appendix E Characteristic Livsic function
  • Appendix F Examples, counterexamples, notes
  • References
  • Index

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