Book contents
- Frontmatter
- Contents
- Foreword
- Lie Algebras and Root Systems
- Lie Groups
- Introduction
- 1 Examples
- 2 SU2, SO3, and SL2ℝ
- 3 Homogeneous spaces
- 4 Some theorems about matrices
- 5 Lie theory
- 6 Representation theory
- 7 Compact groups and integration
- 8 Maximal compact subgroups
- 9 The Peter-Weyl theorem
- 10 Functions on ℝn and Sn-1
- 11 Induced representations
- 12 The complexification of a compact group
- 13 The unitary and symmetric groups
- 14 The Borel-Weil theorem
- 15 Representations of non-compact groups
- 16 Representations of SL2ℝ
- 17 The Heisenberg group
- Linear Algebraic Groups
- Notes and references
- Bibliography
- Index
3 - Homogeneous spaces
Published online by Cambridge University Press: 05 June 2012
Foreword by
Book contents
- Frontmatter
- Contents
- Foreword
- Lie Algebras and Root Systems
- Lie Groups
- Introduction
- 1 Examples
- 2 SU2, SO3, and SL2ℝ
- 3 Homogeneous spaces
- 4 Some theorems about matrices
- 5 Lie theory
- 6 Representation theory
- 7 Compact groups and integration
- 8 Maximal compact subgroups
- 9 The Peter-Weyl theorem
- 10 Functions on ℝn and Sn-1
- 11 Induced representations
- 12 The complexification of a compact group
- 13 The unitary and symmetric groups
- 14 The Borel-Weil theorem
- 15 Representations of non-compact groups
- 16 Representations of SL2ℝ
- 17 The Heisenberg group
- Linear Algebraic Groups
- Notes and references
- Bibliography
- Index
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Lectures on Lie Groups and Lie Algebras , pp. 59 - 62Publisher: Cambridge University PressPrint publication year: 1995