First BGG operators via homogeneous examples

Abstract

We review the theory of first BGG operators and study how to approach them and find their solution on homogeneous geometries. We provide many new examples of parabolic geometries that admit solutions of first BGG operators with many interesting properties and interpretations.

arXiv comment50 pp, comments welcome

References in corpus (12)

• Prolongations of Geometric Overdetermined Systems
• Einstein metrics in projective geometry
• Holonomy reductions of Cartan geometries and curved orbit decompositions
• Homogeneous Levi non-degenerate hypersurfaces in ${\mathbb{C}}^3$
• C-projective geometry
• Curved Casimir Operators and the BGG Machinery
• Relative BGG sequences; II. BGG machinery and invariant operators
• The Geometry of Almost Einstein (2,3,5) Distributions
• Submaximally symmetric c-projective structures
• Homogeneous integrable Legendrian contact structures in dimension five
• First BGG operators on homogeneous conformal geometries
• Homogeneous Real (2,3,5) Distributions with Isotropy