# SMRI Algebra and Geometry Online

commutative algebra algebraic geometry analysis of PDEs algebraic topology differential geometry general topology geometric topology metric geometry operator algebras quantum algebra rings and algebras symplectic geometry

Sydney Mathematical Research Institute

Audience: | Researchers in the topic |

Seminar series times: | No fixed schedule |

Organizer: | SMRIAdmin* |

*contact for this listing |

SMRI Algebra and Geometry Online

‘Tits groups of Iwahori-Weyl groups and presentations of Hecke algebras’

Xuhua He (Chinese University of Hong Kong)

Thursday 5th August, 3:30pm - 5:00pm (AEST)

Register: uni-sydney.zoom.us/meeting/register/tZYtcu-przouH9zYrbDw_tL7yC9JirzOWzZH

Abstract: Let G(ℂ) be a complex reductive group and W be its Weyl group. In 1966, Tits introduced a certain subgroup of G(ℂ), which is an extension of W by an elementary abelian 𝟸-group. This group is called the Tits group and provides a nice lifting of W. In this talk, I will discuss a generalization of the notion of the Tits group 𝒯 to a reductive p-adic group G. Such 𝒯, if exists, gives a nice lifting of the Iwahori-Weyl group of G. I will show that the Tits group exists when the reductive group splits over an unramified extension of the p-adic field and will provide an example in the ramified case that such a Tits group does not exist. Finally, as an application, we will provide a nice presentation of the Hecke algebra of the p-adic group G with In-level structure. Based on the recent joint work with Ganapathy (arXiv:2107.01768).

Biography: Xuhua He received his PhD from MIT in 2005. After postdoctoral positions at the IAS and Stony Brook University, He was an A/Professor at HKUST from 2008 and a Full Professor at the University of Maryland from 2014 before joining CUHK in 2019 as Choh-Ming Professor of Mathematics. He received the Morningside Gold Medal of Mathematics in 2013 and the Xplorer Prize in 2020, and was an invited sectional speaker of the International Congress of Mathematicians in 2018.

Note: These seminars will be recorded, including participant questions (participants only when asking questions), and uploaded to the SMRI YouTube Channel www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI

Other upcoming SMRI events can be found here: mathematical-research-institute.sydney.edu.au/seminars/

Your time | Speaker | Title | |||
---|---|---|---|---|---|

Thu | Aug 05 | 05:30 | Xuhua He | Tits groups of Iwahori-Weyl groups and presentations of Hecke algebras |

Your time | Speaker | Title | |||
---|---|---|---|---|---|

Fri | Jul 23 | 01:00 | Shrawan Kumar | Root components for tensor product of affine Kac-Moody Lie algebra modules | |

Thu | Jul 08 | 05:30 | Ulrich Thiel | Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution | |

Wed | Jun 23 | 23:00 | Gus Lonergan | 'Geometric Satake over KU' | |

Thu | Jun 17 | 05:30 | Magdalena Boos | Advertising symmetric quivers and their representations | |

Thu | May 06 | 05:30 | Shun-Jen Cheng | ‘Representation theory of exceptional Lie superalgebras | |

Thu | Feb 25 | 23:00 | Monica Nevins | Characters and types: the personality of a representation of a p-adic group, revealed by branching to its compact open subgroups |