Corollary 2

The $\mathfrak{g}$-modules $E(\lambda )$ for $\lambda \in P_{++}$ constitute a set of representatives of the classes of finite dimensional simple $\mathfrak{g}$-modules.

The $\mathfrak{g}$-modules $E(\lambda )$, where $\lambda$ is a fundamental weight, are called the fundamental $\mathfrak{g}$-modules; the corresponding representations are called the fundamental representations of $\mathfrak{g}$; they are absolutely irreducible (§6, no. 2, Prop. 3 (iv)).

If V is a finite dimensional $\mathfrak{g}$-module and $\lambda \in P_{++}$, the isotypical component of V of type $E(\lambda )$ is called the isotypical component of highest weight $\lambda$ of V.