Equivariant quantizations for AHS--structures

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.

19 pages, no figures

References in corpus (2)

• Curved Casimir Operators and the BGG Machinery
• Invariant Bilinear Differential Pairings on Parabolic Geometries

Cited by in corpus (10)

• Higher Symmetries of the Laplacian via Quantization
• Second Order Symmetries of the Conformal Laplacian
• Projectively equivariant quantizations over the superspace ${\mathbb{R}}^{p|q}$
• Conformally Equivariant Quantization - a Complete Classification
• On osp(p+1,q+1|2r)-equivariant quantizations
• Higher symmetries of the conformal powers of the Laplacian on conformally flat manifolds
• spo(2|2)-Equivariant Quantizations on the Supercircle $S^{1|2}$
• Quantization and injective submodules of differential operator modules
• Equivariant quantization of spin systems
• Conformally equivariant quantization and symbol maps associated with $n$-ary differential operators on weighted densities