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The pro- $p$ -Iwahori Hecke algebra of a reductive $p$ -adic group I

Published online by Cambridge University Press:  23 October 2015

Marie-France Vigneras
Affiliation:
Institut de Mathematiques de Jussieu, 175 rue du Chevaleret, Paris 75013, France email vigneras@math.jussieu.fr
Corresponding
E-mail address:

Abstract

Let $R$ be a commutative ring, let $F$ be a locally compact non-archimedean field of finite residual field $k$ of characteristic $p$ , and let $\mathbf{G}$ be a connected reductive $F$ -group. We show that the pro- $p$ -Iwahori Hecke $R$ -algebra of $G=\mathbf{G}(F)$ admits a presentation similar to the Iwahori–Matsumoto presentation of the Iwahori Hecke algebra of a Chevalley group, and alcove walk bases satisfying Bernstein relations. This was previously known only for a $F$ -split group $\mathbf{G}$ .

Type
Research Article
Copyright
© The Author 2015 

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