Winter Term 2023

Lior Silberman
- Office: MATX 1112, 604-827-3031
- Email: "lior" (at) Math.UBC.CA (please include the course number in the subject line, if applicable)
- Office hours (Winter 2022): by appointment or
Time Location Zoom Meeting ID Zoom Password MF 11:30-12:30 My office and Zoom 691 7826 7667 761818 Wed 21:30-22:30 Zoom only 682 2985 1665 155350

- Classes: MWF 14:00-15:00 at ESB 4127 and on Zoom.
- Syllabus.
- (Rough) lecture notes (updated 12/3/2023).

This is the second course in our Lie Theory sequence. I shall discuss the structre and representation theory of real Lie groups.

- BrÃ¶cker–tom Dieck, Representations of Compact Lie Groups
- Knapp, Lie Groups Beyond an Introduction

*Warning: the following information is tentative and subject to change at any time*

Week | Date | Material | In-class | Notes |
---|---|---|---|---|

1 | M 9/1 | Introduction | Scan | |

W 11/1 | Topological groups; representations | Scan | ||

F 13/1 | Basic constructions | Scan | ||

2 | M 16/1 | Compact groups | Scan | |

W 18/1 | G-finite vectors | Scan | ||

F 20/1 | The Peter--Weyl Theorem | Scan | ||

3 | M 23/1 | Manifolds | Scan | |

W 25/1 | Tangent and Cotangent spaces | Scan | ||

F 27/1 | Lie Groups | Scan | ||

4 | M 30/1 | Lie algebras | Scan | |

W 1/2 | The exponential map | Scan | ||

F 3/2 | Closed subgroups | Scan | ||

5 | M 6/2 | The adjoint representation | Scan | |

W 8/2 | Compact Lie groups; tori | Scan | ||

F 10/2 | Centralizers of tori | Scan | ||

6 | M 13/2 | Maximal tori | Scan | |

W 15/2 | SU(2); weights | Scan | ||

F 17/2 | Roots | Scan | ||

20/2–25/2 | Winter break | |||

7 | M 27/2 | Groups of rank 1 | Scan | |

W 1/3 | The algebraic Weyl group | Scan | ||

F 3/3 | Weyl Chambers | Scan | ||

8 | M 6/3 | Root Systems | Scan | |

W 8/3 | The dual Weyl chamber | Scan | ||

F 10/3 | Represetation theory of SU(2) | Scan | ||

9 | M 13/3 | (continued) | Scan | |

W 15/3 | The universal enveloping algebra | Scan | ||

F 17/3 | Highest weights | |||

10 | M 20/3 | |||

W 22/3 | Verma modules | |||

F 24/3 |

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