An arbitrary proper parabolic subalgebra ${ \mathfrak p}$ of a simple complex Lie algebra ${ \mathfrak g}$ induces an embedding ${ \mathfrak g}\hookrightarrow \mathbb W_n$, and more generally an embedding ${ \mathfrak g}\hookrightarrow \mathbb W_n\otimes \operatorname{ End}{ } V$, where $\mathbb W_n$ is the Weyl algebra in $n$ variables, $n$ is the dimension of the nilradical of ${ \mathfrak p}$, and $V$ is an arbitrary ${ \mathfrak p}$-module. We give an elementary proof of this known fact, report on a computer program computing the embeddings, and tabulate exceptional Lie algebra embeddings $G_2 \hookrightarrow \mathbb W_5$, $F_4 \hookrightarrow \mathbb W_{ 15}$, $E_6 \hookrightarrow \mathbb W_{ 16}$, $E_7 \hookrightarrow\mathbb W_{ 27}$, $E_8 \hookrightarrow \mathbb W_{ 57}$ arising in this fashion.
Categories: math.RT