# NCG

## Seminar

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

Seminar Room 1, Newton Institute

#### 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.