# weight lattice

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 . 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 $\mathfrak{g}$.

Title weight lattice WeightLattice 2013-03-22 13:11:57 2013-03-22 13:11:57 bwebste (988) bwebste (988) 9 bwebste (988) Definition msc 17B20 integral weight