Details of MA4204 (Spring 2023)
| Level: 4 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4204 | Representation Theory of Finite Groups | Swarnendu Datta |
| Syllabus |
|---|
| Representations of Finite Groups: Definitions, Schurs theorem, characters, group algebra,
Maschkes theorem, simple modules over group algebras, inner products of characters, the number of irreducible characters, character tables and orthogonality relations, Burnsides two-prime theorem, Induced representation, Frobenius reciprocity, construction of character tables of GL(2, k), SL(2, k), P GL(2, k) where k is a finite field. Further Topics: Brauers theorem on induced characters, representation of symmetric groups, Young diagrams and Frobenius character formula. |
| Prerequisite |
|---|
| Linear Algebra II (MA3104) and Algebra II (MA3203). |
| References |
|---|
| Suggested Texts:
1. Fulton, W. and Harris, J., Representation Theory : A First Course, Springer-Verlag. 2. James, G. and Liebeck, M., Representations and Characters of Groups, Cambridge University Press. 3. Musili, C., Representations of Finite Groups, Hindustan Book Agency. 4. Serre, J.P., Linear Representation of Finite Groups, Springer. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP | 4 | Not Allowed |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Not Allowed |
| 11 | MS | 8 | Elective |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |