| Jan 6 | Definitions and basic operations for linear representations of finite groups (1.1, 1.2) |
| Jan 8 | Irreducible representations (1.3) |
| Jan 10 | Characters (1.4) |
| Jan 13 | Classification of representations (1.5) Examples (1.6) |
| Jan 15 | Examples (1.6) Group algebra (1.7) |
| Jan 17 | Restriction and induction (1.8) Partitions (2.1) |
| Jan 20 | no class |
| Jan 22 | Tabloids (2.2) Specht modules (2.3) |
| Jan 24 | Specht modules (2.3) |
| Jan 27 |
Garnir relations and standard tableaux (2.4) HW1 due |
| Jan 29 | Symmetric functions definitions (3.1) Monomial symmetric functions (3.2) |
| Jan 31 | Elementary symmetric functions (3.3) Involution ω (3.4) Complete homogeneous symmetric functions (3.5) |
| Feb 3 | Power sum symmetric functions (3.6) Scalar product (3.7) |
| Feb 5 |
Scalar product (3.7) Symmetric groups (5.1) Frobenius characteristic map (5.2) |
| Feb 7 |
Frobenius characteristic map (5.2) Semistandard Young tableaux (4.1) |
| Feb 10 |
RSK algorithm (4.2) HW2 due |
| Feb 12 |
Dual RSK algorithm (4.3) Determinantal formula (4.4) |
| Feb 14 | Multiplying Schur functions (4.5) |
| Feb 17 | no class |
| Feb 19 | no class HW3 due |
| Feb 21 | Jacobi-Trudi identity (4.6) |
| Feb 24 | Murnaghan-Nakayama rule (5.3) |
| Feb 26 | Murnaghan-Nakayama rule (5.3) Formula for # standard Young tableaux (6.1) |
| Feb 28 |
Formula for # standard Young tableaux (6.1) Formula for # semistandard Young tableaux (6.2) |
| Mar 2 |
Littlewood-Richardson coefficients HW4 due |
| Mar 4 | Polynomial representations of the general linear group |
| Mar 6 | Polynomial representations of the general linear group |
| Mar 9 | Schur modules |
| Mar 11 | Polynomial functors |
| Mar 13 | Schur-Weyl duality |