LOOP GROUPS

by Pressley, Andrew; Segal, Graeme

• ISBN13: 9780198535614
• ISBN10: 0198535619
• Edition: 1st
• Format: Paperback
• Copyright: 1988-06-16
• Publisher: Oxford

Summary

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.

Table of Contents

Introduction

Finite Dimensional Lie Groups

Groups of Smooth Maps

Central Extensions

The Root System: Kac-Moody Algebras

Loop Groups as Groups of Operators in Hilbert Space

The Grasmannian of Hilbert Space and the Determinant Time Bundle

The Fundamental Homogeneous Space

Representation Theory

The Fundamental Representation

The Borel-Weil Theory

The Spin Representation

'Blips' or 'Vertex-Operators'

The Kac Character Formula and the Bernstein-Gelfand-Gelfand Resolution

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