MTL739 Representation of Finite Groups

Credits: 3 (3-0-0)

Prerequisites: MTL105/MTL501

Description

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).

Prerequisite Tree

flowchart TD
MTL739-1008[MTL739]
MTL739-1008 --- Or1009[Any one of]:::empty
Or1009 -.-> MTL105-1010[MTL105]
Or1009 -.-> MTL501-1011[MTL501]

classDef empty height:17px, fill:transparent, stroke:transparent;
classDef trueEmpty height:0px, width:0px;