Equivariant functions and rational differential operators

TL;DR

This paper explores the use of contact geometry to characterize the monoid of projectively equivariant meromorphic differential operators on complex curves, extending classical equivariant quantization to non-commutative algebras.

Contribution

It introduces a geometric framework for understanding equivariant differential operators and generalizes classical quantization methods to non-commutative settings.

Findings

Describes the monoid of equivariant meromorphic differential operators using contact geometry.

Provides a quantization approach that extends classical equivariants to non-commutative algebras.

Establishes a new link between contact geometry and the theory of differential operators.

Abstract

We use contact geometry to describe the monoid of projectively equivariant meromorphic differential operators on a complex curve, quantization of which generalizes known constructions of classical equivariants to non-commutative function algebras in several variables.