2024/2025 (Autumn) Topics in Mathematical Science VII
Course themeIntroduction to finite group representations
Preliminary lecture plan
| Week | Date | Topic |
|---|---|---|
| 1 | 10-03 | Overview. Definition (group rep, homomorphisms). Examples. |
| 2 | 10-10 | Group algebra and modules. Indecomposable and irreducible. |
| 3 | 10-17 | Maschke's Theorem. Schur's lemma. |
| 4 | 10-24 | Rep's of fintie abelian groups. Decomposing regular rep. |
| 5 | 10-31 | Dual rep. Tensor rep. |
| 6 | 11-07 | Characters. Conjugacy classes. |
| 7 | 11-14 | Class function. Inner product. |
| 8 | 11-23 | Orthogonality. Inflations. |
| 9 | 11-28 | Restriction, Clifford theory. |
| 10 | 12-05 | Induction. Frobenius reciprocity. Mackey's formula. |
| 11 | 12-12 | Revision / Catch-up / Q&A |
| 12 | 12-19 | Symmetric group, partitions, Young diagrams, tableaux, tabloids |
| 13 | 12-26 | Specht modules |
| 14 | 01-02 | NO LECTURE (Winter break) |
| 15 | 01-09 | RSK correspondence |
| 16 | 01-16 | Cellular algebras and Weyl groups |
Time and Venue Thursday 13:00–14:30, Grad. School of Mathematics Room 409
Evaluation
- There is no examination. Grading is evaluated through homework assignments.
- In each assignment, the 2 highest scoring question will be recorded.
- Final grading is determined by the average of the 5 highest recorded marks.
- Grading scheme is as follows.
- A : 85 ∼ 100%
- B : 70 ∼ 84%
- C : 50 ∼ 69%
- Fail : 0 ∼ 49%
References (In order of preferences)
- G. James and M. Liebeck: Representations and characters of groups 2nd ed, Cambridge University Press, 2001
- K. Erdmann and T. Holm: Algebras and representation theory. Springer Undergraduate Mathematics Series, Springer International Publishing, 2018
- A. Zimmermann: Representation Theory: A Homological Algebra Point of View,