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SUMMARY:Iwahori-Hecke algebras and measures for split Kac-Moody groups - R
 amla Abdellatif (Université de Picardie Jules Verne)
DTSTART:20181120T143000Z
DTEND:20181120T153000Z
UID:TALK109318@talks.cam.ac.uk
CONTACT:Beth Romano
DESCRIPTION:Let p be a prime integer. Studying complex smooth representati
 ons of a p-adic group G requires various tools of different natures\, as i
 nduction functors\, Hecke algebras (seen as convolution algebras or as int
 ertwinning algebras) or Bruhat-Tits buildings\, that are strongly related 
 to each other. \nIn this talk\, we will first review which of these object
 s 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 expl
 ain why the existing Iwahori-Hecke algebra is not fully satisfying in gene
 ral\, 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 Hec
 ke algebras generalizing those existing for reductive groups. All these re
 sults require to use the masure of the group G (due to Gaussent-Rousseau a
 nd Rousseau)\, and come from a joint work with Auguste Hébert.
LOCATION:MR13
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