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Ramla Abdellatif (Université de Picardie Jules Verne)
Tuesday 20 November 2018, 14:30-15:30
Iwahori-Hecke algebras and measures for split Kac-Moody groups
- 👤 Speaker: Ramla Abdellatif (Université de Picardie Jules Verne)
- 📅 Date & Time: Tuesday 20 November 2018, 14:30 - 15:30
- 📍 Venue: MR13
Abstract
Let p be a prime integer. Studying complex smooth representations of a p-adic group G requires various tools of different natures, as induction functors, Hecke algebras (seen as convolution algebras or as intertwinning algebras) or Bruhat-Tits buildings, that are strongly related to each other. In this talk, we will first review which of these objects have a counterpart when G is a split Kac-Moody group defined over a non-archimedean local field with finite residue class field. Then we will explain why the existing Iwahori-Hecke algebra is not fully satisfying in general, and what can be done to fill in some gaps. If time permits, we will also explain how to define, for split Kac-Moody groups, a family of Hecke algebras generalizing those existing for reductive groups. All these results require to use the masure of the group G (due to Gaussent-Rousseau and Rousseau), and come from a joint work with Auguste Hébert.
Series This talk is part of the Number Theory Seminar series.
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