First BGG operators on homogeneous conformal geometries

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Authors

GREGOROVIČ Jan ZALABOVÁ Lenka

Year of publication 2023
Type Article in Periodical
Magazine / Source Classical and Quantum Gravity
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1088/1361-6382/acbc05
Doi http://dx.doi.org/10.1088/1361-6382/acbc05
Keywords homogeneous conformal geometry; first BGG operator; conformal Killing tensors; twistor spinors; conformal Killing-Yano forms; Godel metric; conformal circles
Description We study first BGG operators and their solutions on homogeneous conformal geometries. We focus on conformal Killing tensors, conformal Killing-Yano forms and twistor spinors in particular. We develop an invariant calculus that allows us to find solutions explicitly using only algebraic computations. We also discuss applications to holonomy reductions and conserved quantities of conformal circles. We demonstrate our result on examples of homogeneous conformal geometries coming mostly from general relativity.
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