Details of MA5117 (Autumn 2020)

Level: 5 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(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.ProgrammeSemester NoCourse 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