Erratum to "Completed Iwahori-Hecke algebra and parahoric Hecke algebras for Kac-Moody groups over local fields"
Résumé
We modify the definition of the completed Iwahori-Hecke algebra given in our previous article (J. Ec. Polytechnique 6, 79-118) and explain why the construction we gave earlier is not correct as such. The goal of this erratum is to fix the construction of the completed Iwahori-Hecke algebra given in [AH19, Section 4.4], as the definition given there does not always provide an actual algebra (see Section 2 below). We define here an algebra that must be used instead. Consequently, the following modifications should be operated in [AH19] : the paragraph before [AH19, Proposition 4.33] is wrong and must be replaced by Section 3 below; Theorem 4.21, Corollary 4.23 and Theorem 4.30 of [AH19] are wrong as stated there and must respectively be replaced by Theorem 3.12, Corollary 3.13 and Theorem 3.14 below.
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Est requise par hal-01536067 Article Ramla Abdellatif, Auguste Hébert. Completed Iwahori-Hecke algebras and parahoric Hecke algebras for Kac-Moody groups over local fields. Journal de l'École polytechnique — Mathématiques, 2019, 6, pp.79-118. ⟨10.5802/jep.88⟩. ⟨hal-01536067v3⟩