Details of MA5117 (Autumn 2020)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5117 | Representation Theory of Finite Groups | Soumalya Joardar |
| Syllabus |
|---|
| Representation Theory of Finite Groups: Definitions, Schur's theorem, characters, group algebra, Maschke's theorem, simple modules over group algebras, inner products of characters, the number of irreducible characters, character tables and orthogonality relations, Burnside's two-prime theorem, Induced representation, Frobenius reciprocity, construction of character tables of $GL(2,k), SL(2,k), PGL(2,k)$ for a finite field $k$.
Further Topics: Brauer's 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, Hindusthan Book Agency. 4. Serre, J.P. Linear Representation of Finite Groups, Springer. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MR | 1 | Not Allowed |
| 5 | MR | 3 | Not Allowed |
| 6 | MS | 5 | Not Allowed |
| 7 | MS | 7 | Elective |
| 8 | MS | 9 | Elective |
| 9 | RS | 1 | Not Allowed |
| 10 | RS | 2 | Not Allowed |