MTL739:Representation of Finite Groups

3 Credits (3-0-0)

Pre-requisites: MTL105/MTL501

Revision of basic group theory. Definition and examples of representation. Subrepresentation, sum and tensor product of represenations, irreducible representations; Character Theory: Character of a representation, Schur’s Lemma, Maschke’s theorem, Orthogonality relations for characters, decomposition of regular representation, number of irreducible representations of a group; Representation of subgroups and product of groups, induced representations; Group Algebra: Representations and modules; Decomposition of complex  algebra C[G] and Integrability properties of characters. Induced representations, restriction to subgroups, Reciprocity formula, Mackey’s irreducibility criterion; Irreducible representations of symmertric groups (S_n) and alternating groups (A_n).