Zero Energy States for SU(N): A Simple Exercise in Group Theory ?

We show that the requirement of $S_3\times Spin(d)$ invariance for a ``asymptotically free'' SU(3)-Cartan subalgebra wave-function does {\em not} give a unique candidate for a SU(3)-invariant zero energy state of the d=9 supersymmetric matrix model - nor does it rule out the existence of such a state in the case d=3. For d=9 we explicitly construct various $S_3\times Spin(9)$-invariant wave-functions.}