| Time | Location | Zoom Meeting ID | Zoom Password |
|---|---|---|---|
| T 9:30-10:00 | ORCH 3009 | N/A | N/A |
| Th 9:30-11:00 | ORCH 3009 and on Zoom | 694 6667 3745 | 914585 |
| F 11:45-13:00 | at PIMS and on Zoom | 676 1308 4912 | 139267 |
This is the second course in our Lie Theory sequence. I shall discuss the structre and representation theory of real Lie groups.
Warning: the following information is tentative and subject to change at any time
| Chapter | Week | Date | Material | In-class | Notes |
|---|---|---|---|---|---|
| Compact topological groups |
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 | |||
| Lie groups | 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 | ||
| Compact Lie groups |
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 | |||
| Representation theory of compact Lie groups |
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 weight thm: uniqueness | Scan | |||
| 10 | M 20/3 | (continued) | Scan | ||
| W 22/3 | Verma modules | Scan | |||
| F 24/3 | Weyl itegration formula | Scan | |||
| 11 | M 27/3 | Weyl character formula | Scan | ||
| Semisimple Lie groups |
W 29/3 | Semisimple Lie algebras | Scan | ||
| F 31/3 | Cartan involutions | Scan | |||
| 12 | M 3/4 | Global Cartan involution | Scan | ||
| W 5/4 | No lecture due to Passover | ||||
| W 12/4 | Symmetric spaces | Scan | |||
| 13 | M 24/4 | Iwasawa decomposition | Scan | ||
| F 28/4 | (continued) | Scan | |||
| Infinite dimensional representations |
14 | M 1/5 | Smooth vectors | Scan | |
| F 5/5 | Scan | ||||
| M 8/5 | The principal series |
|
|
|
Clarification: the writings on these pages are generally my own creations (to which I own the copyright), and are made available for traditional academic reuse. If you wish to republish substantial portions (including in "derivative works") please ask me for permission. The material is expressly excluded from the terms of UBC Policy 81.