{"title":"Rankin-Cohen brackets on tube-type domains","authors":"J. Clerc","doi":"10.2140/tunis.2021.3.551","DOIUrl":null,"url":null,"abstract":"A new formula is obtained for the holomorphic bi-differential operators on tube-type domains which are associated to the decomposition of the tensor product of two scalar holomorphic representations, thus generalizing the classical Rankin-Cohen brackets. The formula involves a family of polynomials of several variables which may be considered as a (weak) generalization of the classical Jacobi polynomials.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"83 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/tunis.2021.3.551","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
A new formula is obtained for the holomorphic bi-differential operators on tube-type domains which are associated to the decomposition of the tensor product of two scalar holomorphic representations, thus generalizing the classical Rankin-Cohen brackets. The formula involves a family of polynomials of several variables which may be considered as a (weak) generalization of the classical Jacobi polynomials.
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