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Compact Lie Groups and Their Representations
About this Title
D. P. Želobenko. Translated by Israel Program for Scientific Translations
Publication: Translations of Mathematical Monographs
Publication Year:
1973; Volume 40
ISBNs: 978-0-8218-1590-8 (print); 978-1-4704-4455-6 (online)
DOI: https://doi.org/10.1090/mmono/040
MathSciNet review: MR1844360
MSC: Primary 47B10; Secondary 47A99
Table of Contents
Front/Back Matter
Chapters
- Preface
- Topological groups. Lie groups
- Linear groups
- Fundamental problems of representation theory
- Compact Lie groups. Global theorem
- The infinitesimal method in representation theory
- Analytic continuation
- Irreducible representations of the group $\mathrm {U}(n)$
- Tensors and Young diagrams
- Casimir operators
- Indicator systems and the Gel′fand-Cetlin basis
- Characters
- Tensor product of two irreducible representations of $\mathrm {U}(n)$
- Basic types of Lie algebras and Lie groups
- Classification of compact and reductive Lie algebras
- Compact Lie groups in the large
- Description of irreducible finite-dimensonal representations
- Infinitesimal theory (characters, weights, Casimir operators)
- Some problems of spectral analysis for finite-dimensional representations