On Lorentz invariance and supersymmetry of four particle scattering amplitudes in $S^N\R^8$ orbifold sigma model

The S N R 8 supersymmetric orbifold sigma model is expected to describe the IR limit of the Matrix string theory. In the framework of the model the type IIA string interaction is governed by a vertex which was recently proposed by R.Dijkgraaf, E.Verlinde and H.Verlinde. By using this interaction vertex we derive all four particle scattering amplitudes directly from the orbifold model in the large N limit.