{"title":"Holomorphic Laplacian on the Lie ball and the Penrose transform","authors":"Hideko Sekiguchi","doi":"10.1016/j.indag.2024.04.004","DOIUrl":null,"url":null,"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.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1016/j.indag.2024.04.004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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