M402: Representations of Finite Groups
Syllabus:
- Group representations
- Maschke’s theorem and completely reducibility
- Characters, Inner product of Characters, Orthogonality relations
- Burnside’s theorem
- induced characters, Frobenius reciprocity, induced
representations, Mackey’s Irreducibility Criterion
- Character table of some well-known groups
- Representation theory of the symmetric group: partitions and
tableaux, constructing the irreducible representations.
References:
- G. James, M. Liebeck, “Representations and
Characters of Groups”, Cambridge University Press, 2010.
- B. Steinberg, “Representation Theory of Finite
Groups”, Universitext, Springer, 2012.
- J.-P. Serre, “Linear Representations of Finite
Groups”, Graduate Texts in Mathematics 42, Springer-Verlag, 1977.
Lectures:
- Monday [T] (14.30--15.30)
- Tuesday (16.30--17.30)
- Wednesday (15.30--16.30)
- Thursday (14.30--15.30)
Assignment:
- Assignment 1
- Assignment 2
- Assignment 3
- Assignment 4
- Assignment 5
- Assignment 6
Quiz:
Examination:
- Mid-Semester
- End-Semester
Evaluation Procedure for Grading:
There will be two quizzes carrying 15
marks each, a mid-semester examination of 30 marks and one
final end-Semester exam of 40 marks (Total 100). The final grading will
be done based on the performance in the quizzes, mid-semester and
end-semester examination. Suppose the total marks obtained by
a student is X out of 100. Then the grading will be as
follows:
- 0<=X< 30---FR
- 30<=X<40---DD
- 40<=X<50---CD
- 50<=X<60---CC
- 60<=X<70---BC
- 70<=X<80---BB
- 80<=X<90---AB
- 90<=X<=100---AA
Keys to Success:
Attend all the lectures and tutorials, Do the homeworks, ask
questions. Talk to me if you have any problem.