I am organizing a regular seminar on Weyl/Coxter group, Springer theory, Hecke algebra and related topics.

## 2018-Spring Representations of Finite group and affine Hecke algebra

For 2018 Spring semester, from 28 Feb 2018 to the end of the semester.

**Time:** Wednesday afternoon **13:00-15:30**, Week 1-17.

**Venue:** School of Mathematics SJTU, Room-1106.

We plan to read the following two papers.

1. Pierre Deligne and George Lusztig, Representations of Reductive Groups Over Finite Fields

2. David Kazhdan, George Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras

The tasks are divied as the following:

Speackers | Deligne-Lusztig’s paper |
---|---|

Ma Jiajun | Introduction, Section 1-2 |

Chen Miaofen | Section 3-4 |

TBA | Section 5 |

TBA | Section 6-7 |

TBA | Section 8-9 |

TBA | Section 10-11 |

Speackers | Kazhdan-Lusztig’s paper |
---|---|

TBA | TBA |

## 2017-Fall Minimal length elements

For 2017 Fall semester, from 11-Sep 2017 to 21-Nov 2017, the time and venue are as the following:

**Time:** Wednesday afternoon **13:00-15:00**.

**Venue:** School of Mathematics SJTU, Room-1106.

Time/speaker | Venue | Title/Abstract |
---|---|---|

Sep 13, 2017, 13:00-15:00 | Room-1106 | Introduction on conjugacy classes of finite coxeter groups. |

Ma Jia-Jun | We will discuss the geometric interpretation of the length function of finite Coxeter groups. | |

Sep 20, 2017, 13:00-15:00/Ma Jia-Jun | Room-1106 | Geometric interpretation of the length function. (cont.) |

Sep 27, 2017, 14:00-15:00/Ma Jia-Jun | Room-1106 | Proof of the main theorem on minimal length elements (for finite Coxeter group) |

Oct 4, 2017 | Cancelled due to the national day holiday. | |

Oct 11, 2017 | Cancelled due to an event of the department. | |

Oct 18, 13:00-15:00/Zhang Guanglian | Room-1106 | Elliptic elements in Weyl groups |

Oct 25, 13:00-15:00/Zhang Guanglian | Room-1106 | Good elements in Weyl groups |

Nov 1, 13:00-15:00/Qin Fan | Room-1106 | Introduction to affine Weyl groups. |

Nov 8, 13:00-15:00/Qin Fan | Room-1106 | minimal length element in affine groups. |

Nov 15, 13:00-15:00/Qin Fan | Room-1106 | minimal length element in affine groups (cont.) |

Nov 22 | Cancelled | |

Nov 29 13:00-15:00/Chen Miaofen | Room-1106 | Straight conjugacy class |

Dec 6 13:00-15:00/Chen Miaofen | Room-1106 | Straight conjugacy class and its relation to other topics. |

Dec 13: 13:00-15:00/ Ma Jia-Jun | Room-1106 | Classification of nice elements. |

Dec 20 10:00-12:00/ Ma Jia-Jun | Room-1106 | Cocenter of an affine Hecke algebra. |

## 2017-Spring Springer theory

For 2017 Spring semester, from 21-Mar 2017 to 27-June 2017, the time and venue are as the following:

**Time:** Tuesday noon **12:00-13:30**. (the time slot is updated)

**Venue:** School of Mathematics SJTU, Room-1106.

Time | Venue | Title/Abstract |
---|---|---|

Mar 21, 2017, 18:30-20:00 | Room-1106 | Introduction to Springer theory |

This is the first talk of my proposed seminar on Weyl group, Springer theory, Hecke algebra and related topics. As an orientation, I will first explain the content of Springer correspondence. Then I will briefly review the basic idea of the constructions of the Springer correspondence. In the end, I will discuss some relationships of the Springer theory with other fields, such as combinatorics and representation theory of reductive groups. If time permits, I will also discuss the generalized Springer correspondence. | ||

Mar 28, 2017 | Canceled | |

April 4, 2017 | Canceled due to Qingming Festival | |

April 11, 2017, 12:00-13:30 | Room-1106 | A proof of Springer correspondence by Chriss-Ginzburg, (I) |

I will present a proof of the Springer correspondence following Chriss-Ginzburg's book "Representation Theory and Complex Geometry" in the next two or three talks. In this talk, I plan to discuss the geometry of the flag variety and the Steinberg variety. | ||

April 18, 2017, 12:00-13:30 | Room-1106 | |

Continue the discussion on Ghriss-Ginzburg's book. | ||

April 25, 2017, 12:00-13:30 | Room-1106 | |

Continue the discussion on Ghriss-Ginzburg's book. | ||

May 2 , 2017, 12:00-13:30 | Canceled | |

May 9 , 2017, 12:00-13:30 | Room-1106 | Discussion on Ghriss-Ginzburg's book: Borel-Moore homology |

May 16 , 2017, 12:00-13:30 | Room-1106 | Discussion on Ghriss-Ginzburg's book: Borel-Moore homology |

May 23 , 2017, 12:00-13:30 | Room-1106 | Discussion on Ghriss-Ginzburg's book. |

May 30 , 2017, 12:00-13:30 | Canceled due to Duanwu Festival(Dragon Boat Festival) | |

Jun 6 , 2017, 12:00-13:30 | Discussion on Ghriss-Ginzburg's book. | |

Jun 13 , 2017, 12:00-13:30 | Discussion on Ghriss-Ginzburg's book. | |

Jun 20 , 2017, 12:00-13:30 | Discussion on Ghriss-Ginzburg's book. Finished Chapter 3 |