Normal forms of irreducible sl3-valued zero curvature representations

One of the ways to overcome existing limitations of the famous Wahlquist-Estabrook procedure consists in employing normal forms of zero curvature representations (ZCR). While in case of sľ2 normal forms are known for a long time, the next step is made in this paper. We find normal forms of sľ3-valued ZCR that are not reducible to a proper subalgebra of sľ3. We also prove a reducibility theorem, which says that if one of the matrices in a ZCR (A, B) falls into a proper subalgebra of sľ3, then the second matrix either falls into the same subalgebra or the ZCR is in a sense trivial. In the end of this paper we show examples of ZCR and their normal forms.