The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

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.