Center of ${\mathcal{H}}_R(0,c_{\tilde{s}})$ associated to a pro-$p$-Iwahori Weyl group

Abstract

Let $W$ be an Iwahori Weyl group and $W(1)$ be an extension of $W$ by an abelian group. Vigneras gave a description of the $R$-algebra ${\mathcal{H}}_R(q_{\tilde{s}},c_{\tilde{s}})$ associated to $W(1)$, and also gave a basis of the center of ${\mathcal{H}}_R(q_{\tilde{s}},c_{\tilde{s}})$ using the Bernstein presentation of ${\mathcal{H}}_R(q_{\tilde{s}},c_{\tilde{s}})$. In this paper, we restrict to the case where $q_{\tilde{s}}=0$ and use the Iwahori-Matsumoto presentation to give a basis of the center of ${\mathcal{H}}_R(0,c_{\tilde{s}})$.

19 pages