  The theory of quantum symmetric pairs provides a universal K-matrix which is
an analogue of the universal R-matrix for quantum groups. The main ingredient
in the construction of the universal K-matrix is a quasi K-matrix which has so
far only been constructed recursively. In this paper we restrict to the cases
where the underlying Lie algebra is sl(n) or the Satake diagram has no black
dots. In these cases we give an explicit formula for the quasi K-matrix as a
product of quasi K-matrices for Satake diagrams of rank one. This factorisation
depends on the restricted Weyl group of the underlying symmetric Lie algebra in
the same way as the factorisation of the quasi R-matrix depends on the Weyl
group of the Lie algebra. We conjecture that our formula holds in general.
