Conformally invariant differential operators on Minkowski space and their curved analogues
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Publication:1112349
DOI10.1007/BF01215221zbMath0659.53047OpenAlexW2020404846MaRDI QIDQ1112349
John W. Rice, Michael G. Eastwood
Publication date: 1987
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01215221
Verma modulesconformally invariant differential operatorsmassless field equationsPenrose's local twistor transport
Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Invariance and symmetry properties for PDEs on manifolds (58J70) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)
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Cites Work
- Unnamed Item
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- Homogeneous vector bundles
- A conformally invariant Maxwell gauge.
- A comparison theory for the structure of induced representations
- Cohomology and massless fields
- Representations of real reductive Lie groups
- A generalization of the Bernstein-Gelfand-Gelfand resolution
- A comparison theory for the structure of induced representations. II
- Complexification, twistor theory and harmonic maps from Riemann surfaces
- A Duality for Homogeneous Bundles on Twistor Space
- Spaces of Complex Null Geodesics in Complex-Riemannian Geometry
- A High–Low search game on the unit interval
- The generalized Penrose-Ward transform
- CONFORMALLY INVARIANT FIRST ORDER DIFFERENTIAL OPERATORS
- Edth-a differential operator on the sphere
- Zero rest-mass fields including gravitation: asymptotic behaviour
- Structure of certain induced representations of complex semisimple Lie algebras
- Conformal tensors
- Twistor Algebra
- Overdetermined systems of linear partial differential equations
- Introduction to Lie Algebras and Representation Theory
- On Some Applications of the Universal Enveloping Algebra of a Semisimple Lie Algebra