2000/01/31 by David M. J. Calderbank, Tammo Diemer · 1 citation
Mathematics · Physics and Astronomy · #math.DG #math-ph #math.MP #math.RT #msc:53A55 #msc:16E45 #msc:17B55 #msc:53A30 #msc:53C15 #msc:53C28 #msc:58A32
published as J.Reine Angew.Math. 537 (2001) 67-103 · AMS-LaTeX 31 pages; improved proof of A-infinity stuff; references added; corrected deformation theory discussion
arxiv created 2000/02/15 · arxiv updated 2009/11/30
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.