Strongly isotropy irreducible spaces whose Laplacians have all their eigenspaces irreducible

Let $H$ be a closed subgroup of a compact connected Lie group $G$ such that $G/H$ is simply connected, the action of $G$ on $G/H$ is almost effective, and $G/H$ is a strongly isotropy irreducible space. The smallest positive eigenvalue of the Laplace-Beltrami operator $Δ$ associated to the standard