Completed Iwahori-Hecke algebras and parahoric Hecke algebras for Kac-Moody groups over local fields
Algèbres d’Iwahori-Hecke complétées et algèbres de Hecke parahoriques pour les groupes de Kac-Moody sur les corps locaux
Résumé
Let G be a split Kac-Moody group over a non-archimedean local field. We define a completion of the Iwahori-Hecke algebra of G. We determine its center and prove that it is isomorphic to the spherical Hecke algebra of G using the Satake isomorphism. This is thus similar to the situation of reductive groups. Our main tool is the masure I associated to this setting, which is the analogue of the Bruhat-Tits building for reductive groups. Then, for each special and spherical facet F , we associate a Hecke algebra. In the Kac-Moody setting, this construction was known only for the spherical subgroup and for the Iwahori subgroup.
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Requiert hal-04206162 Article Ramla Abdellatif, Auguste Hébert. Erratum to Completed Iwahori-Hecke algebra and parahoric Hecke algebras for Kac-Moody groups over local fields. Journal de l'École polytechnique — Mathématiques, 2022, 9, pp.1293-1304. ⟨10.5802/jep.206⟩. ⟨hal-04206162⟩