An extension of the Borel-Weil construction to the quantum group U q(n)

The Borel-Weil (BW) construction for unitary irreps of a compact Lie group is extended to a construction of all unitary irreps of the quantum group U q(n). This q-BW construction uses a recursion procedure for U q(n) in which the fiber of the bundle carries an irrep of U q(n-1)×U q(1) with sections that are holomorphic functions in the homogeneous space U q(n)/U q(n-1)×U q(1). Explicit results are obtained for the U q(n) irreps and for the related isomorphism of quantum group algebras.