Čap, Andreas; Salač, Tomáš

Parabolic Conformally Symplectic Structures. III: Invariant Differential Operators and Complexes

Doc. Math. 24, 2203-2240 (2019)
DOI: 10.25537/dm.2019v24.2203-2240
Communicated by Christian Bär

Summary

This is the last part of a series of articles on a family of geometric structures (PACS-structures) which all have an underlying almost conformally symplectic structure. While the first part of the series was devoted to the general study of these structures, the second part focused on the case that the underlying structure is conformally symplectic (PCS-structures). In that case, we obtained a close relation to parabolic contact structures via a concept of parabolic contactification. It was also shown that special symplectic connections (and thus all connections of exotic symplectic holonomy) arise as the canonical connection of such a structure. \par In this last part, we use parabolic contactifications and constructions related to Bernstein-Gelfand-Gelfand (BGG) sequences for parabolic contact structures, to construct sequences of differential operators naturally associated to a PCS-structure. In particular, this gives rise to a large family of complexes of differential operators associated to a special symplectic connection. In some cases, large families of complexes for more general instances of PCS-structures are obtained.

Mathematics Subject Classification

53D05, 53D10, 53C15, 58J10, 53C10, 53C55, 58A10

Keywords/Phrases

parabolic geometry, conformally symplectic structure, invariant differential operator, differential complex, BGG sequence

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Affiliation

Čap, Andreas
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria
Salač, Tomáš
Mathematical Institute, Charles University, Prague, Czech Republic

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