标题： 第一BGG算子在齐次共形几何上 显示英文标题

标题： First BGG operators on homogeneous conformal geometries

摘要： 我们首先研究齐次共形几何上的BGG算子及其解。 我们特别关注共形Killing张量、共形Killing-Yano形式和扭旋矢量。 我们开发了一种不变微积分，使我们能够仅通过代数计算显式地找到解。 我们还讨论了其在全纯约化和共形圆的守恒量中的应用。 我们在主要来自广义相对论的齐次共形几何示例中展示了我们的结果。 显示英文摘要

摘要： 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.