Irreducible and decomposable representation
Maschke’s theorem
Schur’s Lemma
Schur Orthogonality relations
Characters and class functions
Regular Representations
Character Table
Permutation representations
Irreducible representation of S_4
Irreducible representation of dihedral groups
Centralizer Algebra and Gelfand Pairs
Symmetric Gelfand Pairs
Tensor products of representations
Frobenius reciprocity
Induced Representations
Mackey’s irreducible criteria
Partition function and Young diagrams
Young tableux and tabloids
Specht representations of symmetric groups