Representation Theory
Schedules
Course contents for Representation Theory : MTH 410/514/620
- Representations of groups, subrepresentations, Irreducible representations, tensor product of representations, Maschke's theorem, Wedderburn decomposition.
- Characters of representations, Generalized characters, Schurs lemma, Orthogonality, Regular representations, Decomposition theorems.
- Representations of direct product of finite groups, Induced representations, Reciprocity theorem.
- Representations and characters of standard finite and infinite groups: cyclic groups, dihedral groups, symmetric and alternating groups of small order etc.
- Applications of Representation Theory.
Homeworks
Quizzes
Exams
Reference texts for the course
Character theory of finite groups, I.M. Isaacs, AMS Chelsea.
Finite Groups, D. Gorenstein, AMS Chelsea.
Linear representations of finite groups, J-P. Serre, GTM 42, Springer.
Representation theory: a first course, W. Fulton, J. Harris, GTM 129, Springer.
Representations and cheracters of groups, G. James, M. Liebeck.
Group theory II, M. Suzuki, Springer.
Groups and representations, J.L. Alperin, R.B. Bell, GTM 162, Springer.