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Other titles in the Oxford Mathematical Monographs series:
Loop Groups (Oxford Mathematical Monographs)by Andrew Pressley
Synopses & ReviewsPublisher Comments:Loop groups, the simplest class of infinite dimensional Lie groups, have recently been the subject of intense study. This book gives a complete and selfcontained 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 developedalgebra, 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.
Synopsis:This book gives a complete and selfcontained 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.
Description:Includes bibliographical references (p. [304]310).
Table of Contents1. Introduction
PART I 2. Finite Dimensional Lie Groups 3. Groups of Smooth Maps 4. Central Extensions 5. The Root System: KacMoody 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 PART II 9. Representation Theory 10. The Fundamental Representation 11. The BorelWeil Theory 12. The Spin Representation 13. 'Blips' or 'VertexOperators' 14. The Kac Character Formula and the BernsteinGelfandGelfand Resolution What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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