Abstract: To any strongly $k$-rational representation $\pi$ of a connected reductive algebraic group $G$ defined over a number field $k$, we attach a constant $\gamma_\pi$ as an analog of Hermite's constant, and we give a lower estimate of $\gamma_\pi$ in the case that the stabilier of the highest weight space of $\pi$ in $G$ is a maximal parabolic subgroup.
Full text of the article: