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Subcomplexes in curved BGG-sequences

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Abstract

BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the compositions of the operators in such a sequence are nonzero. In this paper, we show that under appropriate torsion freeness and/or semi-flatness assumptions certain parts of all BGG sequences are complexes. Several examples of structures, including quaternionic structures, hypersurface type CR structures and quaternionic contact structures are discussed in detail. In the case of quaternionic structures we show that several families of complexes obtained in this way are elliptic.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090, Wien, Austria

    Andreas Čap

  2. Mathematical Institute, Charles University, Sokolovská 83, Praha, Czech Republic

    Vladimír Souček

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  1. Andreas Čap
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  2. Vladimír Souček
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Correspondence to Andreas Čap.

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Čap, A., Souček, V. Subcomplexes in curved BGG-sequences. Math. Ann. 354, 111–136 (2012). https://doi.org/10.1007/s00208-011-0726-4

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  • DOI: https://doi.org/10.1007/s00208-011-0726-4

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