Representation Theory

Representations of Finite Groups

1. Group Actions & Modulesrepresentations, invariant subspaces, irreducibility9.5–16.5 h
2. Characterscharacter theory, orthogonality relations, decomposition9.5–16.5 h
3. Induced Representations & Frobenius Reciprocityinduction, restriction, Mackey theory intro9.5–16.5 h

Lie Theory & Applications

1. Representations of S_n and GL(n)Young tableaux, symmetric functions intro9.5–16.5 h
2. Lie Groups & Lie Algebras Representations Introweights, highest weight theorem, SU(2) and spin9.5–16.5 h
3. Applications to Physicsparticle multiplets, angular momentum coupling, symmetry breaking9.5–16.5 h