Bernstein-Gelfand-Gelfand sequences

By Andreas Čap, J. Slovák, V. Souček. 2000

262 citations recorded by the source corpus.

The Bernstein-Gelfand-Gelfand sequences extend the complexes of homogeneous vector bundles to curved Cartan geometries.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Pathology and Forensic Medicine

View Paper: https://www.semanticscholar.org/paper/9cda5acba53e9bf8575486ff3f036ad85b981363

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Andreas Čap
2. Michael Eastwood
3. D. Calderbank
4. T. Diemer
5. T. Branson
6. Rod A. Gover
7. A. Gover
8. F. Burstall

In Mathematical Physics

1. Andreas Čap
2. D. Calderbank
3. T. Diemer
4. A. Gover
5. Michael Eastwood
6. C. Graham

In Pathology and Forensic Medicine

1. Andreas Čap
2. D. Calderbank
3. T. Diemer
4. Michael Eastwood

Citations in the corpus

• Two constructions with parabolic geometries (2005, unknown): “It follows from the general machinery of BGG–sequences, see [14, 6].”
• CR-Tractors and the Fefferman Space (2006, background): “All these facts are an extremely special case of the machinery of BGG sequences, whose general version has been developed in [12] and [6].”
• Correspondence spaces and twistor spaces for parabolic geometries (2001, background): “2) of [11] the second summand gives −(n + 1)Z·f , so the claim follows.”
• PROLONGATIONS OF GEOMETRIC OVERDETERMINED SYSTEMS (2004, background): “Gelfand-Gelfand (BGG) resolution’ and one motivation for our study comes from analogues of these first operators on almost Hermitian symmetric manifolds [1] or, more generally, on parabolic geometries [3, 5]. By construction, these analogues are invariant linear differential operators having the same ”
• Ricci-corrected derivatives and invariant differential operators (2003, background): “Various special cases of the main results of this section can be found in [7, 16, 17, 22, 32].”
• Higher symmetries of the laplacian (2002, background): “ally invariant. In fact, the differential operator that is the left hand side of (1) is the first operator in a conformally invariant complex of operators known as the Bernstein-Gelfand-Gelfand complex [3, 5, 7, 11, 29]. This implies that the conformal Killing tensors on Rn form an irreducible represe”
• Equivalence and embedding problems for CR-structures of any codimension (2001, background): “[22] and Čap and Schmalz [21] for certain Levi-nondegenerate CR-manifolds of higher codimension and by Ebenfelt [28] for certain uniformly Levi-degenerate hypersurfaces in C3.”
• Infinitesimal automorphisms and deformations of parabolic geometries (2005, methodology): “The machinery of Bernstein–Gelfand–Gelfand sequences (or BGG sequences), which was introduced in [13] and improved in [5], can be applied to this twisted de Rham sequence.”
• Di erential invariants and curved Bernstein-Gelfand-Gelfand sequences (2000, methodology): “The AHS structures have been extensively studied by Čap, Slovák and Souček in [17, 18, 19], and in the last paper of this series they construct a large class of invariant differential operators for these geometries.”
• Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “for example [FG85], [ CSS01 ], [CD01], [E05], [J06]).”