基本信息

书名:表示论和复几何

定价：59.00元

作者:(美)克里斯　著

出版社：世界图书出版公司

出版日期：2012_01_01

ISBN：9787510040573

字数：

页码：495

版次：1

装帧：平装

开本：24开

商品重量：

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　　克里斯编著的《表示论和复几何（英文版）》是一部经典的从集合角度讲述表示论的高等教程。从几何的角度研究表示论，真可谓“千呼万呼始出来”，尤其是自从1980年D_模型和1990年量子群的箭图，此方法显得更为迫切。表示论的发展顺应科学发展趋势，并且都成功地应用于好多领域，如量子群、仿射李群和量子场论。本书的前半部分是架起李理论标准知识初学者和数学工作者所需要的广阔背景知识之间的桥梁，为后半部分的学习做好充分的准备。

内容提要

目录

preface
chapter 0. introduction
chapter 1. symplectic geometry
　1.1. symplectic manifolds
　1.2. poisson algebras
　1.3. poisson structures arising from noncommutative algebras
　1.4. the moment map
　1.5. coisotropic subvarieties
　1.6. lagrangian families
chapter 2. mosaic
　2.1. hilbert's nullste!lensatz
　2.2. atone algebraic varieties
　2.3. the deformation construction
　2.4. c*_actions on a projective variety
　2.5. fixed point reduction
　2.6. borel_moore homology
　2.7. convolution in borel_moore homology
chapter 3. complex semisimple groups
　3.1. semisimple lie algebras and flag varieties
　3.2. nilpotent cone
　3.3. the steinberg variety
　3.4. lagrangian construction of the weyl group
　3.5. geometric analysis of h(z)_action
　3.6. irreducible representations of we~1 groups
　3.7. applications of the jacobson_morozov theorem
chapter 4. springer theory for u(sln)
　4.1. geometric construction of the enveloping algebrau(sin(c))
　4.2. finite_dimensional simple sln(c)_modules
　4.3. proof of the main theorem
　4.4. stabilization
chapter 5. equivariant k_theory
　5.1. equivariant resolutions
　5.2. basic k_theoretic constructions
　5.3. specialization in equivariant k_theory
　5.4. the koszul complex and the thom isomorphism
　5.5. cellular fibration lemma
　5.6. the k/inneth formula
　5.7. projective bundle theorem and beilinson resolution
　5.8. the chern character
　5.9. the dimension filtration and ""devissage""
　5.10. the localization theorem
　5.11. functoriality
chapter 6. flag varieties, k_theory, and harmonic polynomials
　6.1. equivariant k_theory of the flag variety
　6.2. equivariant k_theory of the steinberg variety
　6.3. harmonic polynomials
　6.4. w_harmonic polynomials and flag varieties
　6.5. orbital varieties
　6.6. the equivariant hilbert polynomial
　6.7. kostant's theorem on polynomial rings
chapter 7. hecke algebras and k_theory
　7.1. affine weyl groups and hecke algebras
　7.2. main theorems
　7.3. case q = h deformation argument
　7.4. hilbert polynomials and orbital varieties
　7.5. the hecke algebra for sl2
　7.6. pwof of the main theorem
chapter 8. representations of convolution algebras
　8.1. standard modules
　8.2. character formula for standard modules
　8.3. constructible complexes
　8.4. perverse sheaves and the classification theorem
　8.5. the contravariant form
　8.6. shed_theoretic analysis of the convolution algebra
　8.7. projective modules over convolution algebra
　8.8. a non_vanishing result
　8.9. semi_small maps
　bibliography

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