Quantization of Projective Homogeneous Spaces and Duality Principle

TL;DR

This paper presents a method to construct quantum projective homogeneous spaces, such as quantum Grassmannians and flag varieties, and extends the quantum duality principle to these spaces, broadening the scope of quantum geometry.

Contribution

It introduces a general construction for quantum projective homogeneous spaces and extends the quantum duality principle to these new quantum spaces.

Findings

Constructed quantum projective homogeneous spaces including quantum Grassmannians.

Extended the quantum duality principle to quantum projective homogeneous spaces.

Provided a framework for future research in quantum geometry and representation theory.

Abstract

We introduce a general recipe to construct quantum projective homogeneous spaces, with a particular interest for the examples of the quantum Grassmannians and the quantum generalized flag varieties. Using this construction, we extend the quantum duality principle to quantum projective homogeneous spaces.