Penrose Transform (eBook)

Robert J. Baston, Michael G. Eastwood (Autoren)

eBook Download: EPUB

2016
256 Seiten
Dover Publications (Verlag)
978-0-486-81662-3 (ISBN)

Infos

Geared toward students of physics and mathematics; presupposes no familiarity with twistor theory. "A huge amount of information, well organized and condensed into less than 200 pages." — Mathematical Reviews. 1989 edition.

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"e;Brings to the reader a huge amount of information, well organized and condensed into less than two hundred pages."e; — Mathematical ReviewsIn recent decades twistor theory has become an important focus for students of mathematical physics. Central to twistor theory is the geometrical transform known as the Penrose transform, named for its groundbreaking developer. Geared toward students of physics and mathematics, this advanced text explores the Penrose transform and presupposes no background in twistor theory and a minimal familiarity with representation theory. An introductory chapter sketches the development of the Penrose transform, followed by reviews of Lie algebras and flag manifolds, representation theory and homogeneous vector bundles, and the Weyl group and the Bott-Borel-Weil theorem. Succeeding chapters explore the Penrose transform in terms of the Bernstein-Gelfand-Gelfand resolution, followed by worked examples, constructions of unitary representations, and module structures on cohomology. The treatment concludes with a review of constructions and suggests further avenues for research.

Autor

Robert J. Baston was on the faculty of The Mathematical Institute, University of Oxford. Michael G. Eastwood is Professor of Mathematics at the Mathematical Sciences Institute, Australian National University, Canberra.

Inhalt

1. Introduction2. Lie Algebras and Flag Manifolds3. Homogeneous Vector Bundles on G/P4. The Weyl Group, its Actions, and Hasse Diagrams5. The Bott-Borel-Weil Theorem6. Realizations of G/P7. The Penrose Transform8. The Bernstein-Gelfand-Gelfand Resolution9. The Penrose Transformation in Practice10. Constructing Unitary Representations11. Module Structures on Cohomology12. Conclusion and Outlook

Produkt-Details

• Erscheint lt. Verlag: 28.10.2016
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 150 x 150 mm
• Gewicht: 369 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: bernstein-gelfand-gelfand resolution • books on math • bott-borel-weil theorem • cohomology • Complex • Differential Geometry • flag manifolds • geometrical transform • Geometry • Homogeneous vector bundles • Lie Algebras • Mathematical Physics • mathematical studies • math resource • Non-fiction • penrose transform • Physics • Representation of groups • Representation Theory • science and math • Twistor theory • Weyl Group
• ISBN-10: 0-486-81662-1 / 0486816621
• ISBN-13: 978-0-486-81662-3 / 9780486816623