Categories of symmetries and infinite-dimensional groups
著者
書誌事項
Categories of symmetries and infinite-dimensional groups
（London Mathematical Society monographs, new ser.,
Clarendon Press , Oxford University Press, 1996
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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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