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Journal of Lie Theory, Vol. 10, No. 1, pp. 33-52 (2000)
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On an analog of Hermite's constant

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Takao Watanabe

Department of Mathematics

Graduate School of Science

Osaka University

Toyonaka, Osaka, 560-0043

Japan

watanabe@math.wani.osaka-u.ac.jp

**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.

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