Lie groups
著者
書誌事項
Lie groups
（Graduate texts in mathematics, 225）
Springer, c2004
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注記
Includes bibliographical references (p. [438]-445) and index
内容説明・目次
内容説明
This book proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and offers a carefully chosen range of material designed to give readers the bigger picture. It explores compact Lie groups through a number of proofs and culminates in a "topics" section that takes the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as unifying them.
目次
Haar Measure.- Schur Orthogonality.- Compact Operators.- The Peter-Weyl Theorem.- Lie Subgroups of GL(n, C).- Vector Fields.- Left Invariant Vector Fields.- The Exponential Map.- Tensors and Universal Properties.- The Universal Enveloping Algebra.- Extension of Scalars.- Representations of sl(2, C).- The Universal Cover.- The Local Frobenius Theorem.- Tori.- Geodesics and Maximal Tori.- Topological Proof of Cartan?s Theorem.- The Weyl Integration Formula.- The Root System.- Examples of Root Systems.- Abstract Weyl Groups.- The Fundamental Group.- Semisimple Compact Groups.- Highest Weight Vectors.- The Weyl Character Formula.- Spin.- Complexification.- Coxeter Groups.- The Iwasawa Decomposition.- The Bruhat Decomposition.- Symmetric Spaces.- Relative Root Systems.- Embeddings of Lie Groups.- Mackey Theory.- Characters of GL(n, C).- Duality between Sk and GL(n, C).- The Jacobi-Trudi Identity.- Schur Polynomials and GL(n, C).- Schur Polynomials and Sk.- Random Matrix Theory.- Minors of Toeplitz Matrices.- Branching Formulae and Tableaux.- The Cauchy Identity.- Unitary Branching Rules.- The Involution Model for Sk.- Some Symmetric Algebras.- Gelfand Pairs.- Hecke Algebras.- Cohomology of Grassmannians.
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