Lie groups
This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes 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. The book is organized...
Shranjeno v:
| Glavni avtor: | |
|---|---|
| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
New York, NY :
Springer New York
2013.
Cham : Springer Nature |
| Serija: | Graduate Texts in Mathematics
225 |
| Online dostop: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Sporočilo: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Lie Groups, Texte imprimé, 9781493938421 • Lie Groups, Texte imprimé, 9781461480259 • Lie Groups, Texte imprimé, 9781461480235 |
Kazalo:
- Part I: Compact Topological Groups
- 1 Haar Measure
- 2 Schur Orthogonality
- 3 Compact Operators
- 4 The Peter Weyl Theorem
- Part II: Compact Lie Groups
- 5 Lie Subgroups of GL(n,C)
- 6 Vector Fields
- 7 Left-Invariant Vector Fields
- 8 The Exponential Map
- 9 Tensors and Universal Properties
- 10 The Universal Enveloping Algebra
- 11 Extension of Scalars
- 12 Representations of sl(2,C)
- 13 The Universal Cover
- 14 The Local Frobenius Theorem
- 15 Tori
- 16 Geodesics and Maximal Tori
- 17 The Weyl Integration Formula
- 18 The Root System
- 19 Examples of Root Systems
- 20 Abstract Weyl Groups
- 21 Highest Weight Vectors
- 22 The Weyl Character Formula
- 23 The Fundamental Group
- Part III: Noncompact Lie Groups
- 24 Complexification
- 25 Coxeter Groups
- 26 The Borel Subgroup
- 27 The Bruhat Decomposition
- 28 Symmetric Spaces
- 29 Relative Root Systems
- 30 Embeddings of Lie Groups
- 31 Spin
- Part IV: Duality and Other Topics
- 32 Mackey Theory
- 33 Characters of GL(n,C)
- 34 Duality between Sk and GL(n,C)
- 35 The Jacobi Trudi Identity
- 36 Schur Polynomials and GL(n,C)
- 37 Schur Polynomials and Sk. 38 The Cauchy Identity
- 39 Random Matrix Theory
- 40 Symmetric Group Branching Rules and Tableaux
- 41 Unitary Branching Rules and Tableaux
- 42 Minors of Toeplitz Matrices
- 43 The Involution Model for Sk
- 44 Some Symmetric Alegras
- 45 Gelfand Pairs
- 46 Hecke Algebras
- 47 The Philosophy of Cusp Forms
- 48 Cohomology of Grassmannians
- Appendix: Sage
- References
- Index.