The weight lattice $\Lambda_W$ of a root system $R\subset E$ is the lattice $$\Lambda_W=\left\{ e\in E \left| \frac{(e,\alpha)}{(\alpha,\alpha)}\in\mathbb{Z} \text{ for all } r\in R \right. \right\} .$$ Weights which lie in the weight lattice are called integral. If $R\subset\mathfrak{h}$ is the root system of a semi-simple Lie algebra $\mathfrak{g}$ with Cartan subalgebra $\mathfrak{h}$ then $\Lambda_W$ is exactly the set of weights appearing in finite dimensional representations of $\mathfrak{g}$