Normal and seminormal forms of sl(3)-valued zero curvature representations

Abstract

We find normal and seminormal forms for a sl(3)-valued zero curvature representation (ZCR). We prove a theorem about reducibility of ZCR's, which says that if one of the matrix in a ZCR (A,B) falls to a proper subalgebra of sl(3), then the second matrix either falls to the same subalgebra or the ZCR is almost trivial. In the end of this paper we show examples of ZCR's and their normal forms.