The Penrose Transform Its Interaction with Representation Theory

by Baston, Robert J.; Eastwood, Michael G.

• ISBN13: 9780198535652
• ISBN10: 0198535651
• Format: Hardcover
• Copyright: 1990-01-04
• Publisher: Oxford University Press

Summary

During the past two decades, Roger Penrose's twistor theory has been a continuing source of mathematical inspiration. This ambitious theory aims to reformulate the foundations of physics using conformal and complex geometry. At the heart of twistor theory lies a geometrical transform know as the Penrose transform. This book provides coverage of this transform in a general setting, utilizing complex homogeneous spaces, with mathematical input taken from the representation theory of Lie groups. The Penrose Transform gives readers much original research that is not available in any other text, with special attention to the twistor theory of Minkowski space.

Table of Contents

Introduction

Lie Algebras and Flag Manifolds

Homogeneous Vector Bundles on G/P

The Weyl Group, its Actions, and Hasse Diagrams

The Bott-Borel-Weil Theorem

Realizations of G/P

The Penrose Transform

The Bernstein-Gelfand-Gelfand Resolution

The Penrose Transformation in Practice

Constructing Unitary Representations

Module Structures on Cohomology

Conclusion and Outlook

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