**Text:** Wulf Rossmann, *Lie Groups: An Introduction
Through Linear Groups*,

ISBN 0-19-859683-9,
Oxford University Press, New York, 2002.

Date | Lecture | Reading | Topics |
---|---|---|---|

1/19 | 1 | 1.1 | Vector Fields and one-parameter matrix groups |

1/24 | 2 | 1.2 | The exponential map and its differential |

1/26 | 3 | 1.3 | Campbell-Baker-Hausdorff series |

1/31 | 4 | 2.1 | Linear groups |

2/02 | 5 | 2.1 | Examples of linear groups |

2/07 | 6 | 2.2 | Lie algebra of a linear group |

2/09 | 7 | 2.3 | Exponential coordinates |

2/14 | 8 | 2.3 | Topology and analytic coordinates on linear groups |

2/16 | 9 | 2.4 | Connected linear groups |

2/21 | 10 | 2.5 | Lie algebra--Lie group correspondence |

2/23 | 11 | 2.5 | Classification of abelian Lie groups |

2/28 | 12 | 2.5 | Lie algebra--Lie group dictionary |

3/02 | 13 | 2.5 | Commutator subgroup, Homomorphisms |

3/07 | 14 | 2.6, 2.7 | Coverings of linear groups, Closed subgroups |

3/09 | 15 | 3.1 | Classical groups |

Spring Break | |||

3/21 | 16 | 3.1 | Classical groups |

3/23 | 17 | 3.1 | Polar Decomposition of Classical Groups |

3/28 | 18 | 4.1 | Manifolds |

3/30 | 19 | 4.2 | Homogeneous spaces |

4/04 | 20 | 4.2, 4.3 | Homogeneous spaces and Lie groups |

4/06 | 21 | 5.1 | Integration on manifolds |

4/11 | 22 | 5.2 | Integration on Lie groups and homogeneous spaces |

4/13 | 23 | 5.3 | Conjugacy classes in U(n); Weyl's integral formula for U(n) |

4/18 | 24 | 5.3, 6.1 | Proof of Weyl's integral formula; Representations of compact groups |

4/20 | 25 | 6.2 | Schur's Lemma, Peter-Weyl theorem |

4/25 | 26 | 6.3 | Characters |

4/27 | 27 | 6.4 | Weyl's character formula for U(n) |

5/02 | 28 | 6.5 | Highest weight theorem for U(n) |

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Roe Goodman / goodman "at" math "dot" rutgers "dot" edu / Revised April 17, 2005