= Integrality of representation weights on coroots
{title2=$\mu(h_\alpha)\in\mathbb Z$}
Restrict a finite-dimensional representation of a complex <semisimple Lie algebra> to the <sl2 subalgebra associated with a root> $\alpha$. Its Cartan element is the <coroot> $h_\alpha$. The <classification of finite-dimensional sl2 representations> gives only integer eigenvalues for this element, so every <weight of a representation> has integral value on every coroot. This proves containment of all such representation weights in the <weight lattice>; it does not hold for unrestricted infinite-dimensional modules.
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