MTL739: Difference between revisions
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| credits = 3 | | credits = 3 | ||
| credit_structure = 3-0-0 | | credit_structure = 3-0-0 | ||
| pre_requisites = MTL105/MTL501 | | pre_requisites = [[MTL105]]/[[MTL501]] | ||
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Latest revision as of 16:42, 14 April 2026
| MTL739 | |
|---|---|
| Representation of Finite Groups | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | MTL105/MTL501 |
| Overlaps | |
MTL739 : Representation of Finite Groups
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).