Kirillov orbit method for finite Lazard Lie group

Statement

The Kirillov orbit method is a method that can be used to determine the irreducible representations of a finite Lazard Lie group. The procedure is as follows:

• Let $L$ be the Lazard Lie ring of $G$.
• Denote by ${\hat {L}}$ the Pontryagin dual of $L$, viewed only as an additive abelian group. Note that ${\hat {L}}$ is isomorphic to $L$, but there is no natural isomorphism.
• The natural action of $G$ on $L$ (called the adjoint representation)induces a natural action of $G$ on ${\hat {L}}$ (called the coadjoint representation). The orbits under this action correspond to the irreducible representations. Moreover, the size of any orbit is the square of the degree of the irreducible representation to which it corresponds.