{"title":"Symplectic complexity of reductive group actions","authors":"Avraham Aizenbud, Dmitry Gourevitch","doi":"10.1016/j.indag.2024.03.010","DOIUrl":null,"url":null,"abstract":"Let a complex algebraic reductive group act on a complex algebraic manifold . For a -invariant subvariety of the nilpotent cone we define a notion of -symplectic complexity of . This notion generalizes the notion of complexity defined in Vinberg (1986). We prove several properties of this notion, and relate it to the notion of -complexity defined in Aizenbud and Gourevitch (2024) motivated by its relation with representation theory.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"86 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-16","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.2024.03.010","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
Let a complex algebraic reductive group act on a complex algebraic manifold . For a -invariant subvariety of the nilpotent cone we define a notion of -symplectic complexity of . This notion generalizes the notion of complexity defined in Vinberg (1986). We prove several properties of this notion, and relate it to the notion of -complexity defined in Aizenbud and Gourevitch (2024) motivated by its relation with representation theory.
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