Curved Casimir Operators and the BGG Machinery

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2007
• Main Authors: Cap, A., Soucek, V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147189
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Curved Casimir Operators and the BGG Machinery / A. Cap, V. Soucek // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 18 назв. — англ.

We prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the resulting invariant operators and compute their action on v...