  Given $\Gamma$ a finite subgroup of $\mathbf{SL}_3\mathbb{C}$, we determine
how an arbitrary finite dimensional irreducible representation of
$\mathbf{SL}_3\mathbb{C}$ decomposes under the action of $\Gamma$. To the
subgroup $\Gamma$ we attach a generalized Cartan matrix $C_\Gamma$. Then,
inspired by B. Kostant, we decompose the Coxeter element of the Kac-Moody
algebra attached to $C_\Gamma$ as a product of reflections of a special form,
thereby suggesting an algebraic form for the McKay correspondence in dimension
3.
