The Penrose Transform: Its Interaction with Representation Theory (Paperback)
暫譯: 彭羅斯變換:與表示理論的互動
Robert J. Baston, Michael G. Eastwood
- 出版商: Dover Publications
- 出版日期: 2016-11-16
- 售價: $560
- 貴賓價: 9.8 折 $549
- 語言: 英文
- 頁數: 256
- 裝訂: Paperback
- ISBN: 0486797295
- ISBN-13: 9780486797298
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商品描述
<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.
商品描述(中文翻譯)
內容簡介
「為讀者帶來大量資訊,組織良好且濃縮至不到兩百頁。」— 數學評論
在近幾十年中,扭子理論已成為數學物理學生的重要焦點。扭子理論的核心是被稱為佩恩羅斯變換(Penrose transform)的幾何變換,該變換以其開創性開發者命名。本書針對物理和數學的學生,深入探討佩恩羅斯變換,並不假設讀者具備扭子理論的背景知識,僅需對表示理論有最基本的了解。
本書的介紹章節勾勒了佩恩羅斯變換的發展,隨後回顧了李代數、旗流形、表示理論、齊次向量束、以及魏爾群和博特-博雷爾-維爾定理。接下來的章節則從伯恩斯坦-蓋爾凡德-蓋爾凡德解析的角度探討佩恩羅斯變換,並提供了具體的例子、單位表示的構造,以及在上同調上的模結構。最後,書中對構造進行了回顧,並建議了進一步的研究方向。