  It is shown that central elements in G. Letzter's quantum group analogs of
symmetric pairs lead to solutions of the reflection equation. This clarifies
the relation between Letzter's approach to quantum symmetric pairs and the
approach taken by M. Noumi, T. Sugitani, and M. Dijkhuizen.
  We develop general tools to show that a Noumi-Sugitani-Dijkhuizen type
construction of quantum symmetric pairs can be performed preserving spherical
representations from the classical situation. These tools apply to the
symmetric pair FII and to all symmetric pairs which correspond to an
automorphism of the underlying Dynkin diagram. Hence Noumi-Sugitani-Dijkhuizen
type constructions with desirable properties are possible for various symmetric
pairs for exceptional Lie algebras.
