The Penrose Transform: Its Interaction with Representation Theory (Paperback)

<內容簡介>

"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.

「內容簡介」是一本關於 Penrose 變換的高階數學物理學教材，針對物理學和數學的學生。本書探討了 Penrose 變換，並假設讀者對 twistor 理論沒有背景知識，以及對表示論有最基本的了解。

書中的第一章介紹了 Penrose 變換的發展，接著回顧了李代數和旗流形、表示論和齊次向量丛，以及 Weyl 群和 Bott-Borel-Weil 定理。隨後的章節探討了以 Bernstein-Gelfand-Gelfand 解析為基礎的 Penrose 變換，並提供了實例、單位表示的構造，以及上同調的模結構。最後，本書回顧了構造並提出了進一步的研究方向。

這本書提供了大量的資訊，並將其有條理地縮短到不到兩百頁。