The representation theory of finite groups has been an area of intense research ever since its birth in the late nineteenth century. The theory is an important tool in several branches of mathematics, e.g., geometry, number theory, and combinatorics. Moreover, the unsolved mysteries and conjectures intrinsic to the theory, like the Kronecker problem, are expected to keep it an active area of research.This AIS is about the representation theory of symmetric groups, the theory of symmetric functions, and the polynomial representation theory of general linear groups. It is aimed at those pursuing (or intending to pursue) research in any related area of mathematics (interpreted in a broad sense). Basic facility with linear algebra and algebra will be assumed, but otherwise there are no prerequisites. The book Representation theory: A combinatorial viewpoint by Amritanshu Prasad, one of the organizers, will be the main source of reference.

**Syllabus**

Speaker |
No. of lectures |
Syllabus |

I (KNR) | 6 | Basics of ordinary representation theory Chapter 1 |

II (AP) | 6 | RSK Correspondence; semistandard tableaux; simple representations of the symmetric groups Chapter 2 |

III (AP) | 6 | Representations of the symmetric and alternating groups Chapters 2 and 4 |

IV (SV) | 6 | Symmetric functions Chapter 5 |

V (SV) | 6 | Symmetric functions and representations of symmetric groups Chapter 5 (continued) |

VI (KNR) | 6 | Representations of the general linear groups Chapter 6 |

**Resource persons**

- Amritanshu Prasad (AP)
- K. N. Raghavan (KNR)
- Sankaran Viswanath (SV)

The tutorials will be handled mostly by the resource persons themselves, but we want to keep the option open for using the services of other qualified people (of whom there are many in Chennai).

**Time Table**

Day |
Date |
Lecture 1 09:30–11:00 |
Lecture 2 11:30–13:00 |
Tutorial 1 14:15 to 15:15 |
Tutorial 2 15:45–16:45 |

1 | 12th | I | II | I | II |

2 | 13th | I | II | I | II |

3 | 14th | I | II | I | II |

4 | 15th | I | II | I | II |

5 | 16th | I | II | I | II |

6 | 17th | I | II | I | II |

7 | 19th | III | IV | III | IV |

8 | 20th | III | IV | III | IV |

9 | 21st | III | IV | III | IV |

10 | 22nd | III | IV | III | IV |

11 | 23rd | III | IV | III | IV |

12 | 24th | III | IV | III | IV |

13 | 26th | V | VI | V | VI |

14 | 27th | V | VI | V | VI |

15 | 28th | V | VI | V | VI |

16 | 29th | V | VI | V | VI |

17 | 30th | V | VI | V | VI |

18 | 01st | V | VI | V | VI |