Abstract:
Let $\Phi(G_{k_\mathfrak p},P_{\Theta,k_\mathfrak p},\varphi,K)$ be the ring induced by the homorphism $\varphi\colon P_{\Theta,k_\mathfrak p}\to \operatorname{Aut}K$, where $G_{k_\mathfrak p}$ is the Chevalley group over the field $k_\mathfrak p$ of $\mathfrak p$-adic numbers and $P_{\Theta,k_\mathfrak p}$ is a parabolic sybgroup. In this note we characterize a class of subrings of this ring which are invariant relative to translations by elements of the group $G_{k_\mathfrak p}$.
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