BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Xuhua He (Chinese University of Hong Kong) DTSTART:20210805T053000Z DTEND:20210805T070000Z DTSTAMP:20260412T203235Z UID:SAGO/7 DESCRIPTION:Title: Tit s groups of Iwahori-Weyl groups and presentations of Hecke algebras\nb y Xuhua He (Chinese University of Hong Kong) as part of Algebra Seminar (p resented by SMRI)\n\n\nAbstract\nLet G(ℂ) be a complex reductive group a nd 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. Thi s group is called the Tits group and provides a nice lifting of W. In thi s 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 l ifting of the Iwahori-Weyl group of G. I will show that the Tits group exi sts 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 Ti ts group does not exist. Finally\, as an application\, we will provide a n ice presentation of the Hecke algebra of the p-adic group G with In-level structure. Based on the recent joint work with Ganapathy (arXiv:2107.0176 8).\n LOCATION:https://researchseminars.org/talk/SAGO/7/ END:VEVENT END:VCALENDAR