Let $mathfrak{g}$ be a simple Lie algebra of rank $r$ over $mathbb{C}$, $mathfrak{h} subset mathfrak{g}$ a Cartan subalgebra. We construct a family of $r$ commuting Hermitian operators acting on $mathfrak{h}$ whose eigenvalues are equal to the coordinates of the eigenvectors of the Cartan matrix of $mathfrak{g}$.
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