Geometry of Quantum Homogeneous Vector Bundles and Representation Theory of Quantum Groups I

Details Geometry of Quantum Homogeneous Vector Bundles and Representation Theory of Quantum Groups I Geometry of Quantum Homogeneous Vector Bundles and Representation Theory of Quantum Groups I

1997-05-26

arxiv.org/abs/q-alg/9705016v1

Mathematics

Quantum Algebra

Plain Latex, 34 pages, no figures

Scientific paper

Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections furnish projective modules over algebras of functions on quantum homogeneous spaces. Further properties of the quantum homogeneous vector bundles are investigated, and their applications to the representation theory of quantum groups are explored. In particular, quantum Frobenius reciprocity and a generalized Borel-Weil theorem are established.

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