Mathematical Institute, Silesian University in Opava,

Bezrucovo nam. 13, 746 01 Opava, CZECH REPUBLIC

E-mail: M.Marvan@math.slu.cz

**Reducibility of zero curvature representations with
application to inverse recursion operators**

**Abstract:**

A zero curvature representation (ZCR) taking values in a solvable subalgebra
is equivalent to a chain of conservation laws. A criterion to detect reducibility
of a ZCR to a solvable subalgebra will be presented. Given an inverse recursion
operator in Guthrie form, results lead to a recipe to express it in terms
of *D*^{-1}.