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Other titles in the Oxford Mathematical Monographs series:
Loop Groups (Oxford Mathematical Monographs)by Andrew Pressley
Synopses & Reviews
Loop groups, the simplest class of infinite dimensional Lie groups, have recently been the subject of intense study. This book gives a complete and self-contained account of what is known about them from a geometrical and analytical point of view, drawing together the many branches of mathematics from which current theory developed--algebra, geometry, analysis, combinatorics, and the mathematics of quantum field theory. The authors discuss loop groups' applications to simple particle physics and explain how the mathematics used in connection with loop groups is itself interesting and valuable, thereby making this work accessible to mathematicians in many fields.
This book gives a complete and self-contained account of what is known about this subject and is written from a geometrical and analytical point of view, with quantum field theory very much in mind.
Includes bibliographical references (p. -310).
Table of Contents
2. Finite Dimensional Lie Groups
3. Groups of Smooth Maps
4. Central Extensions
5. The Root System: Kac-Moody Algebras
6. Loop Groups as Groups of Operators in Hilbert Space
7. The Grasmannian of Hilbert Space and the Determinant Time Bundle
8. The Fundamental Homogeneous Space
9. Representation Theory
10. The Fundamental Representation
11. The Borel-Weil Theory
12. The Spin Representation
13. 'Blips' or 'Vertex-Operators'
14. The Kac Character Formula and the Bernstein-Gelfand-Gelfand Resolution
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