Equivariant quantizations for AHS--structures

TL;DR

This paper develops a geometric quantization scheme for AHS-structures, enabling intrinsic, equivariant quantizations for symbols on curved projective and conformal geometries, except at certain critical weights.

Contribution

It introduces an explicit, intrinsic quantization method for AHS-structures that works for a broad class of geometric structures, extending equivariance to curved settings.

Findings

Constructed explicit quantization scheme for AHS-structures

Achieved projectively and conformally equivariant quantizations

Applicable to curved geometries with exceptions at critical weights

Abstract

We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so-called AHS-structure. Outside of a finite set of critical (or resonant) weights, this procedure gives rise to a quantization, which is intrinsic to this geometric structure. In particular, this provides projectively and conformally equivariant quantizations for arbitrary symbols on general (curved) projective and conformal structures.