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

Part of: Representation theory of groups Forms and linear algebraic groups Linear algebraic groups and related topics

Published online by Cambridge University Press:  23 October 2015

Marie-France Vigneras
Marie-France Vigneras*
Affiliation:
Institut de Mathematiques de Jussieu, 175 rue du Chevaleret, Paris 75013, France email [email protected]
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Abstract

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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 $\mathbf{G}$.

Keywords

pro-p-Iwahori Hecke algebraaffine Hecke algebraIwahori Weyl groupreductive p-adic groupparahoric subgroupsalcove walk

MSC classification

Primary: 11E95: $p$-adic theory 20G25: Linear algebraic groups over local fields and their integers 20C08: Hecke algebras and their representations
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 4 , April 2016 , pp. 693 - 753
Copyright
© The Author 2015 

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