Brings to the reader a huge amount of information, well organized and
condensed into less than two hundred pages. -- *Mathematical Reviews
*In 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.