Locally unitary principal series representations of ${\mathrm{GL}}_{d+1}(F)$

Abstract

For a local field $F$ we consider tamely ramified principal series representations $V$ of $G={\mathrm{GL}}_{d+1}(F)$ with coefficients in a finite extension $K$ of ${\mathbb{Q}}_p$. Let $I_0$ be a pro-$p$-Iwahori subgroup in $G$, let $\mathcal{H}(G,I_0)$ denote the corresponding pro-$p$-Iwahori Hecke algebra. If $V$ is locally unitary, i.e. if the $\mathcal{H}(G,I_0)$-module $V^{I_0}$ admits an integral structure, then such an integral structure can be chosen in a particularly well organized manner, in particular its modular reduction can be made completely explicit.

References in corpus (1)

• On the universal module of $p$-adic spherical Hecke algebras