李球上的全态拉普拉斯和彭罗斯变换

Indagationes Mathematicae Pub Date : 2024-04-20 DOI:10.1016/j.indag.2024.04.004

Hideko Sekiguchi

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引用次数: 0

摘要

我们证明，在满足偶数维的Lie球上的任何全形函数，都可以通过各向同性子空间的格拉斯曼的某个域的扭曲线束的多尔贝同调的高维彭罗斯变换唯一地得到。为了克服线束参数为，这一设定所带来的困难，我们使用了代数表示理论中的一些技术。

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Holomorphic Laplacian on the Lie ball and the Penrose transform

We prove that any holomorphic function on the Lie ball of even dimension satisfying is obtained uniquely by the higher-dimensional Penrose transform of a Dolbeault cohomology for a twisted line bundle of a certain domain of the Grassmannian of isotropic subspaces. To overcome the difficulties arising from our setting that the line bundle parameter is , we use some techniques from algebraic representation theory.

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Indagationes Mathematicae

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