REPRESENTATIONS OF U-H(SU(N)) DERIVED FROM QUANTUM FLAG MANIFOLDS

A relationship between quantum flag and Grassmann manifolds is reveale d. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a homomorphism lead s to a left U-h(su(N))-module structure on the algebra generated by qu antum 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 the Leibni z rule, The Leibniz rule is shown to be induced by the dressing transf ormation. For discrete values of parameters occurring in the diagonali zation one can extract finite-dimensional irreducible representations of U-h(su(N)) as cyclic submodules. (C) 1997 American Institute of Phy sics.