Q-differential operators

TL;DR

This paper develops a framework for q-analogues of covariant differential operators on hermitian symmetric spaces, linking them to deformation quantization of quadratic algebras, thus advancing the mathematical understanding of quantum symmetries.

Contribution

It introduces a new framework for q-analogues of differential operators and connects them to deformation quantization of quadratic algebras, providing a novel perspective in quantum geometry.

Findings

Established a framework for q-analogues of covariant differential operators.

Linked q-differential operators to deformation quantization of quadratic algebras.

Provided insights into the structure of quantum symmetries on hermitian symmetric spaces.

Abstract

We set up a framework for discussing `$q$-analogues' of the usual covariant differential operators for hermitian symmetric spaces. This turns out to be directly related to the deformation quantization associated to quadratic algebras satisfying certain conditions introduced by Procesi and De Concini.