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美国数学会经典影印系列:轨道法讲义

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作者A. A. Kirillov

出版社高等教育出版社

ISBN9787040469103

出版时间2017-02

版次1

装帧平装

开本16开

纸张胶版纸

页数408页

定价169元

上书时间2024-05-21

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书名:美国数学会经典影印系列:轨道法讲义
定价：169.00元
作者:A. A. Kirillov
出版社：高等教育出版社
出版日期：2017-02-01
ISBN：9787040469103
字数：
页码：408
版次：1
装帧：平装
开本：16开
商品重量：
编辑推荐
《轨道法讲义(英文版)》由高等教育出版社出版。
内容提要
《轨道法讲义(英文版)》向非专家描述了轨道法的要义，第壹次系统、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。
目录
PrefaceIntroductionChapter 1 Geometry of Coadjoint Orbits1 Basic definitions1.1 Coadjoint representation1.2 Canonical form σΩ2 Symplectic structure on coadjoint orbits21 The first（original）approach2.2 The second（Poisson）approach2.3 The third（symplectic reduction）approach2.4 Integrality condition3 Coatijoint invariant functions3.1 General properties of invariants3.2 Examples4 The moment map4.1 The universal property of eoadjoint orbits4.2 Some particular cases5 Polarizations5.1 Elements of symplectic geometry5.2 Invariant polarizations on homogeneous symplectic man— ifoldsChapter 2 Representations and Orbits of the Heisenberg Group1 Heisenberg Lie algebra and Heisenberg Lie group1.1 Some realizations1.2 Universal enveloping algebra u（b）1.3 The Heisenberg Lie algebra as a contraction2 Canonical commutation relations2.1 Creation and annihilation operators2.2 Two—sided ideals in u（□）2.3 H.Weyl reformulation of CCR2.4 The standard realization of CCR2.5 Other realizations of CCR2.6 Uniqueness theorem3 Representation theory for the Heisenberg group3.1 The unitary dual H3.2 The generalized characters of H3.3 The infinitesimal characters of H3.4 The tensor product of unirreps4 Coadjoint orbits of the Heisenberg group4.1 Description of coadjoint orbits4.2 Symplectic forms on orbits and the Poison structure on □4.3 Projections of eoadjoint orbits5 Orbits and representations5.1 Restriction—induction principle and construction of unirreps5.2 Other rules of the User’s Guide6 Polarizations6.1 Real polarizations6.2 Complex polarizations6.3 Discrete polarizationsChapter 3 The Orbit Method for Nilpotent Lie Groups1 Generalities on nilpotent Lie groups2 Comments on the User’s Guide2.1 The unitary dual2.2 The construction of unirreps2.3 Restriction—induction functors2.4 Generalized characters2.5 Infinitesimal characters2.6 Functional dimension2.7 Plancherel measure3 Worked—out examples3.1 The unitary dual3.2 Construction of unirreps3.3 Restriction functor3.4 Induction functor3.5 Decomposition of a tensor product of two unirreps3.6 Generalized characters3.7 Infinitesimal characters3.8 Functional dimension3.9 Plancherel measure3.10 Other examples4 Ptoofs4.1 Nilpotent groups with 1—dimensional center4.2 The main induction procedure4.3 The image of u（□）and the functional dimension4.4 The existence of generalized characters4.5 Homeomorphism of G and □（G）Chapter 4 Solvable Lie Groups1 Exponential Lie groups1.1 Generalities1.2 Pukanszky condition1.3 Restriction—induction functors1.4 Generalized characters1.5 Infinitesimal characters2 General solvable Lie groups2.1 Tame andwild Lie groups2.2 Tame solvable Lie groups3 Example：The diamond Lie algebra g3.1 The coadjoint orbitsfor g3.2 Representations corresponding to generic orbits3.3 Representations corresponding to cylindrical orbits4 Amendments to other rules4.1 Rules 3—54.2 Rules 6，7，and 10Chapter 5 Compact Lie Groups1 Structure of semisimple compact Lie groups1.1 Compact and complex semisimple groups1.2 Classical and exceptional groups2 Coadjoint orbits for compact Lie groups2.1 Geometry of coadjoint orbits2.2 Topology of coadjoint orbits3 Orbits and representations3.1 Overlook3.2 Weights of a unirrep3.3 Functors Ind and Res3.4 Bore—Weil—Bott theorem3.5 The integral formula for characters3.6 Infinitesimal characters4 Intertwining operatorsChapter 6 Miscellaneous1 Semisimple groups1.1 Complex semisimple groups1.2 Real semisimple groups2 Liegroups of general type2.1 Poincare group2.2 Odd symplectic groups3 Beyond Lie groups3.1 Infinite—dimensiohal groups3.2 p—adic and adelic groups3.3 Finite groups3.4 Supergroups4 Why the orbit method works4.1 Mathematicalargument4.2 Physical argument5 Byproducts and relations to other domains5.1 Moment map5.2 Integrable systems6 Some open problems and subjects for meditation6.1 Functional dimension6.2 Infinitesimal characters6.3 Multiplicities and geometry6.4 Complementary series6.5 Finite groups6.6 Infinite—dimensional groups……Appendix Ⅰ Abstract NonsenseAppendix Ⅱ Smooth ManifoldsAppendix Ⅲ Lie Groups and Homogeneous ManifoldsAppendix Ⅳ Elements of Functional AnalysisAppendix Ⅴ Representation TheoryReferencesIndex
作者介绍
作者：（美国）基里洛夫（A.A Kirillov）
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美国数学会经典影印系列:轨道法讲义

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