Lie groups / Daniel Bump.
"This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compa...
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| Main Author: | |
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| Format: | Ebook |
| Language: | English |
| Published: |
New York :
Springer,
[2013]
|
| Edition: | Second edition. |
| Series: | Graduate texts in mathematics ;
225. |
| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | "This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a "topics" section giving depth to the student's understanding of representation theory, taking the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties. |
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| Physical Description: | 1 online resource (xiii, 551 pages) : illustrations. |
| Format: | Mode of access: World Wide Web. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 1461480248 9781461480242 |
| ISSN: | 0072-5285 ; |