Course syllabus
This page will contain the program of the course. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Program
The schedule of the course is in TimeEdit.
Except for the first week we will have exercise classes on Monday and lectures on Tuesday and Thursday. At the exercise classes, students will present and discuss solutions that they have prepared before the class.
Rough plan
| Week | Chapter | Contents |
|---|---|---|
| 30/8-3/9 | 1-3 | Review of group and ring theory; Modules |
| 6-10/9 | 4 | Tensor products |
| 13-17/9 | 5 | Modules over a PID |
| 20-24/9 | 5 | Canonical forms |
| 27/9-1/10 | 6 | Group representations |
| 4-8/10 | 6 | Group representations |
| 11-15/10 | 7 | Representations of the symmetric group |
| 18-22/10 | 8 | Representations of compact groups |
Detailed plan
| Day | Chapter | Contents/Exercises |
|---|---|---|
| 30/8 | 1 | Review of group theory |
| 31/8 | 2 |
Review of ring theory |
| 2/9 | 3 | Modules |
| 6/9 | 1.2.4, 1.7.4, 1.7.5, 1.7.19, 1.7.21, 2.1.4, 2.2.6, 2.3.7, 2.4.7, 2.4.8 | |
| 7/9 |
3.4 |
Direct sums and exact sequences Tensor product |
| 9/9 | 4.3 |
Antisymmetric and symmetric tensor product |
| 13/9 | 2.2.6, 2.3.7, 2.4.8 3.2.2, 3.5.2, 3.5.3, 3.5.5, 4.1.1, 4.4.1, 4.4.2 |
|
| 14/9 | 5.1-5.2 |
Modules over a PID Note the change of room to Euler! |
| 16/9 | 5.2-5.3 | More on modules over PID |
| 20/9 | 4.2.3, 4.3.1, 4.3.2, 4.4.2, 4.4.12, 5.1.1, 5.2.1, 5.2.2, 5.2.3, 5.2.4 | |
| 21/9 | 5.4 | Canonical forms of matrices |
| 23/9 | 5.5, 6.1-6.2 | Applications to ODE Introduction to group representations |
| 27/9 | 5.4.1, 5.4.2, 5.6.1, 5.6.2, 5.6.4, 5.6.6, 5.6.7, 6.1.1, 6.1.5 | |
| 28/9 | 6.3-6.5 |
Regular representation |
| 30/9 | 6.6-6.8 |
Character tables Fourier transform on finite groups |
| 4/10 | 6.2.1, 6.5.1, 6.5.2, 6.6.2, 6.7.1, 6.8.1, 6.8.5, 6.11.1 | |
| 5/10 | 6.9-6.10 |
Peter-Weyl theorem, Frobenius divisibility Note the change of room to EC! |
| 7/10 | 7.1-7.2 | Representations of the symmetric group |
| 11/10 | 6.10.2, 6.10.5, 7.1.1, 7.1.3, 7.2.1, 7.2.2, 7.2.3, 7.2.5 | |
| 12/10 | 7.3-7.4 | Explicit realization of the representations; Young symmetrizers |
| 14/10 | 7.5-7.6 | Schur-Weyl duality |
| 18/10 | 7.7-7.9 | Characters Note change of rooms to MVL14 |
| 19/10 | 8 | Representations of compact groups |
| 21/10 |
Course evaluation Repetition: I will answer questions and go through some of the following problems: 4.4.4, 4.4.8-4.4.9, 5.6.3, 5.6.5, 6.11.5, 6.11.8, 7.2.7, 7.10.5, 8.1.2, 8.1.3
|
Old exams with solutions
200820.pdf (distance exam because of the pandemic)
Theory checklist
Course summary:
| Date | Details | Due |
|---|---|---|