Quantum Grassmann manifolds

Orbits of the quantum dressing transformation for SUq(N) acting on its solvable dual are introduced. The case is considered when the corresponding classical orbits coincide with Grassmann manifolds. Quantization of the Poisson bracket on a Zariski open subset of the Grassmann manifold yields a *-algebra generated by the quantum coordinate functions. The commutation relations are written in a compact form with the help of the R-matrix. Finite-dimensional irreducible representations of Uh(sl(N, C)) are derived from the *-algebra structure. (orig.)