  A relationship between quantum flag and Grassmann manifolds is revealed. This
enables a formal diagonalization of quantum positive matrices. The requirement
that this diagonalization defines a homomorphism leads to a left \Uh -- module
structure on the algebra generated by quantum antiholomorphic coordinate
functions living on the flag manifold. The module is defined by prescribing the
action on the unit and then extending it to all polynomials using a quantum
version of Leibniz rule. Leibniz rule is shown to be induced by the dressing
transformation. For discrete values of parameters occuring in the
diagonalization one can extract finite-dimensional irreducible representations
of \Uh as cyclic submodules.
