An Isaac Newton Institute Workshop

Trends in Noncommutative Geometry

Noncommutative vector bundles on quantum homogeneous spaces and representations of quantum groups

Author: Ruibin Zhang (University of Sydney)

Abstract

Quantum group equivariant vector bundles on quantum homogeneous spaces are classified. An analogue of Dolbeault cohomology is presented for such noncommutative vector bundles. A quantum version of the Bott-Borel-Weil theorem is discussed within this noncommutative geometric framework, realizing representations of quantized universal enveloping algebras on the cohomology groups.