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.
@article{0001158,
author = {Calderbank, David M. J. and Diemer, Tammo},
title = {Differential invariants and curved Bernstein-Gelfand-Gelfand sequences},
journal = {arXiv},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/0001158}
}
Calderbank, David M. J.; Diemer, Tammo. Differential invariants and curved Bernstein-Gelfand-Gelfand sequences. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0001158/