This semester, 2020 Fall, we will focus on the representation theory of real reductive Lie groups.

Throughout these seminar talks, we hope to clarify the current status of the subject and stimulate collaborations. We expect the speakers to explain the technical details. The audiences are encouraged to interrupt the speaker and raise questions/make comments. Most lectures will be given in Chinese.

Click the title for the videos of the talks.

Time | Conference Id | Speaker | Title | Abstract | Host |
---|---|---|---|---|---|

2020/09/02 | NA | 董超平 | Towards the classification of Dirac series for real classical groups | Prof. Dong will collect the math ingredients pertaining to the classification of Dirac series. In particular, he will mention its relation with unipotent representations. | SJTU |

2020/09/25 2pm-4pm | NA | 白占强 | Gelfand-Kirillov dimensions and associated varieties of highest weight modules | In this talk, I will give some introduction to Gelfand-Kirillov dimensions and associated varieties of highest weight modules of Lie algebras (groups). Then I will talk about our work on GKdim and Associated Varieties of highest weight (Harish-Chandra) modules. | SJTU |

2020/10/09 2pm-3pm | 白占强 | Gelfand-Kirillov dimensions and associated varieties of highest weight modules II | See above | SJTU | |

2020/10/09 3:30pm-4:30pm | 余世霖 | Geometric quantization I | The speaker will introduce the notion of Poisson algebra and deformation quantization | SJTU | |

2020/10/16 2:00pm-3:00pm | 腾讯会议 ID：864 4848 4933 会议密码：1122 | 余世霖 | Geometric quantization II | The speaker will continue his talk last week on the notion of Poisson algebra and deformation quantization. Then he will discuss some results on the quantization of a nilpotent coadjoint orbit of a real reductive Lie group. | SJTU |

2020/10/16 3:30pm-4:30pm | see above | 马家骏 | Associated character formula in Howe correspondence I | I will discuss the joint works with Loke and Barbasch-Sun-Zhu on the formula of the associated character of a local theta lifting (Howe correspondence). Furthermore, I will explain its applications in the construction of unipotent representations and geometric quantization. | XMU |

2020/10/23 2:00pm-3:00pm | see above | 马家骏 | Associated character formula in Howe correspondence II | see above | see above |

2020/10/23 3:30pm-4:30pm | see above | Daniel Wong | On NON-unitary (g,K)-modules for complex simple Lie groups I | We discuss several techniques detecting non-unitarity of representations of complex Lie groups G, such as bottom layer K-types, Dirac inequality and deformation of parameters. These techniques are essential in determining the unitary spectrum of G. We will also briefly mention where the difficulties arise as one applies the same techniques for general real reductive groups. | SJTU |

2020/10/30 2:00pm-3:00pm | Zoom: 61208845721 pass:130094 | Daniel Wong | On NON-unitary (g,K)-modules for complex simple Lie groups II | See above | SJTU |

2020/10/30 3:30pm-4:30pm | Zoom: 61208845721 pass:130094 | Li Ning | On certain invariants for constituents of degenerate principal series of Sp(2n,R) | In this talk, I will describe associated cycles and wave front cycles for irreducible constituents of degenerate principal series of Sp(2n,R), and their relationship with the space of generalized Whittaker models of these representations. This can be achieved by a careful study of Loke-Ma and Gomez-Zhu’s work. | SJTU |