Holomorphic Laplacian on the Lie ball and the Penrose transform

Abstract

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.