轨道法讲义（英文版） [Lectures on the Qrbit Method] 下载 mobi epub pdf 电子书 2024

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　　牛顿将其分析学中的发现用变位的形式进行了加密，破译后的甸子是“Itis worthwhile to solve differential equations”（解偏微分方程很重要）。因此，人们在表达轨道法背后的主要思想时可以说“It is worthwhile tostudy coadjoint orbits”（研究余伴随轨道很重要）。
　　轨道法由作者在1960年代引进，一直是诸多领域中十分有用和强大的工具，这些领域包括：李理论，群表示论，可积系统，复几何和辛几何，以及数学物理。《轨道法讲义（英文版）》向非专家描述了轨道法的要义，di一次系统、详细、自足地阐述了该方法。全书从一个方便的“用户指南”开始，并包含了大量例子。《轨道法讲义（英文版）》可以用作研究生课程的教材，适合非专家用作手册，也适合数学家和理论物理学家做研究时参考。

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目录

Preface
Introduction
Chapter 1 Geometry of Coadjoint Orbits
1 Basic definitions
1．1 Coadjoint representation
1．2 Canonical form σΩ
2 Symplectic structure on coadjoint orbits
2．1 The first（original）approach
2．2 The second（Poisson）approach
2．3 The third（symplectic reduction）approach
2．4 Integrality condition
3 Coatijoint invariant functions
3．1 General properties of invariants
3．2 Examples
4 The moment map
4．1 The universal property of eoadjoint orbits
4．2 Some particular cases
5 Polarizations
5．1 Elements of symplectic geometry
5．2 Invariant polarizations on homogeneous symplectic manifolds

Chapter 2 Representations and Orbits of the Heisenberg Group
Chapter 3 The Orbit Method for Nilpotent Lie Groups
Chapter 4 Solvable Lie Groups
Chapter 5 Compact Lie Groups
Chapter 6 Miscellaneous
Appendix Ⅰ Abstract Nonsense
Appendix Ⅱ Smooth Manifolds
Appendix Ⅲ Lie Groups and Homogeneous Manifolds
Appendix Ⅳ Elements of Functional Analysis
Appendix Ⅴ Representation Theory
References
Index

前言/序言

　　The goal of these lectures is to describe the essence of the orbit method for non-experts and to attract the younger generation of mathematicians to some old and still unsolved problems in representation theory where I believe the orbit method could help.
　　It is said that to become a scientist is the same as to catch a train at full speed. Indeed， while you are learning well-known facts and theories， many new important achievements happen. So， you are always behind the present state of the science. The only way to overcome this obstacle is to "jump"， that is， to learn very quickly and thoroughly some relatively small domain， and have only a general idea about all the rest.
　　So， in my exposition I deliberately skip many details that are not absolutely necessary for understanding the main facts and ideas. The most persistent readers can try to reconstruct these details using other sources. I hope， however， that for the majority of users the book will be sufficiently self-contained.
　　The level of exposition is different in different chapters so that both experts and beginners can find something interesting and useful for them.
　　Some of this material is contained in my book [Ki2] and in the surveys [K15l， [K16]， and [K19]. But a systematic and reasonably self-contained exposition of the orbit method is given here for the first time.
　　I wrote this book simultaneously in English and in Russian. For several reasons the English edition appears later than the Russian one and differs from it in the organization of material.
　　Sergei Gelfand was the initiator of the publication of this book and pushed me hard to finish it in time.
　　Craig Jackson read the English version of the book and made many useful corrections and remarks.
　　The final part of the work on the book was done during my visits to the Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette， France) and the Max Planck Institute of Mathematics (Bonn， Germany). I am very grateful to both institutions for their hospitality.
　　In conclusion I want to thank my teachers， friends， colleagues， and es- pecially my students， from whom I learned so much.
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