Differential invariants and curved Bernstein-Gelfand-Gelfand sequences

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We give a simple construction of the Bernstein-Gelfand-Gelfand sequences of natural differential operators on a manifold equipped with a parabolic geometry. This method permits us to define the additional structure of a bilinear differential cup product on this sequence, satisfying a Leibniz rule up to curvature terms. It is not associative, but is part of an A-infinity algebra of multilinear differential operators, which we also obtain explicitly. We illustrate the construction in the case of conformal differential geometry, where the cup product provides a wide-reaching generalization of helicity raising and lowering for conformally invariant field equations.
AMS-LaTeX 31 pages; improved proof of A-infinity stuff; references added; corrected deformation theory discussion

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Differential Geometry, Mathematical Physics, Representation Theory, 53A55 (Primary); 16E45, 17B55, 53A30, 53C15, 53C28, 58A32 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/58580

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0001158
 http://arxiv.org/abs/math/0001158
 J.Reine Angew.Math. 537 (2001) 67-103

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arXiv