The topics covered in each class will be given in the table below, along with the corresponding sections of the notes.

Date | Notes | Topics |
---|---|---|

Jan 10 | 1.1–1.3 | The symmetric group, partitions and compositions, graded rings |

Jan 12 | 1.3, 1.4 | Graded rings (cont.), formal power series |

Jan 17 | 1.4, 2.1, 2.2 | Formal power series (cont.), symmetric polynomials, symmetric functions |

Jan 19 | 2.2, 2.3, 2.4 | Symmetric functions (cont.), tableaux, elementary symmetric functions |

Jan 24 | 2.4, 2.5 | Elementary symmetric functions (cont.), homogeneous symmetric functions |

Jan 26 | 2.6 | Power sums |

Jan 31 | 3.1, 3.2 | Alternating functions, Schur functions |

Feb 2 | 3.2, 3.3 | Jacobi–Trudi identities, the Hall inner product |

Feb 7 | 3.3, 3.4 | The Hall inner product (cont.), skew Schur functions |

Feb 9 | 3.4 | Tableaux description of skew Schur functions |

Feb 14 | 3.5 | Transition matrices |

Feb 16 | 3.6 | The Littlewood–Richardson rule |

Feb 21–25 | Reading week | |

Feb 28 | 4.1, 4.2 | Tensor products, adjoint operators |

Mar 2 | 4.2, 4.3 | Adjoint operators (cont.), Hopf algebras |

Mar 7 | 4.3, 4.4 | Hopf algebras (cont.), Hopf algebra structure on the ring of symmetric functions |

Mar 9 | 4.4, 3.7 | Hopf algebra structure on the ring of symmetric functions (cont.), the Murnaghan–Nakayama rule |

Mar 14 | 5.1, 5.2 | The Heisenberg algebra, bosonic Fock space |

Mar 16 | 5.3 | Fermionic Fock space |

Mar 21 | 5.4 | Bosonization |

Mar 23 | 5.5 | Fermionization |

Mar 28 | 6.1, 6.2 | Characters of finite groups, induction and restriction |

Mar 30 | 6.3 | Characters of the symmetric group |

Apr 4 | 6.4 | Specht modules |

Apr 6 | 6.5 | Representations of the general linear group |