Journal of Lie Theory 35 (2025), No. 1, 165--190
Copyright Heldermann Verlag 2025
Transverse Parabolic Structures and Transverse BGG Sequences
Clémen Cren
Mathematisches Institut, Georg-August Universitaet, Goettingen, Germany
clement.cren@mathematik.uni-goettingen.de
Manifolds endowed with a parabolic geometry in the sense of Cartan come with natural sequences of differential operators and their analysis provide the so called (curved) BGG sequence of Cap, Slovak and Soucek. The sequences involved do not form an elliptic complex in the sense of Atiyah but enjoy similar properties. The proper framework to study these operators is the filtered calculus associated to the natural filtration of the tangent bundle induced by the parabolic geometry. Such analysis was carried over by Dave and Haller in a very general setting. In this article we use their methods associated with the transversal index theory for filtered manifolds developed by the author in a previous paper to derive curved BGG sequences for foliated manifolds with transverse parabolic geometry.
Keywords: Bernstein-Gelfand-Gelfand operators, foliation, parabolic geometry, pseudodifferential calculus, analysis on Lie groups.
MSC: 58H05, 58A10; 58A14, 58A30, 58J22.
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