Group representation theory MOC
The application of representation theory to Group theory MOC studies groups via their representations as linear maps. The main category of interest here is Category of group representations.
Scope of group representation theory results
Fundamentals
- Group representation, Equivalence of group representations
- Group character, Character table
- Reducibility of representations, Decomposition of a representation (Maschke’s theorem)
- Group ring
Schur’s orthogonalities
- Schur’s lemma (general)
- Orthonormality of irreps (finite, compact)
- Orthonormality of irreducible characters (finite, compact)
- Irreducible orthonormal basis
Theorems
Irrep operations
Linear objects
- Generalized projection operator of a representation
- Representation operator (i.e. irreducible operators)