{"title":"Which Schubert Varieties are Hessenberg Varieties?","authors":"Laura Escobar, Martha Precup, John Shareshian","doi":"10.1007/s00031-023-09825-0","DOIUrl":null,"url":null,"abstract":"<p>After proving that every Schubert variety in the full flag variety of a complex reductive group <i>G</i> is a general Hessenberg variety, we show that not all such Schubert varieties are adjoint Hessenberg varieties. In fact, in types A and C, we provide pattern avoidance criteria implying that the proportion of Schubert varieties that are adjoint Hessenberg varieties approaches zero as the rank of <i>G</i> increases. We show also that in type A, some Schubert varieties are not isomorphic to any adjoint Hessenberg variety.</p>","PeriodicalId":49423,"journal":{"name":"Transformation Groups","volume":"61 2","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transformation Groups","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00031-023-09825-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
After proving that every Schubert variety in the full flag variety of a complex reductive group G is a general Hessenberg variety, we show that not all such Schubert varieties are adjoint Hessenberg varieties. In fact, in types A and C, we provide pattern avoidance criteria implying that the proportion of Schubert varieties that are adjoint Hessenberg varieties approaches zero as the rank of G increases. We show also that in type A, some Schubert varieties are not isomorphic to any adjoint Hessenberg variety.
期刊介绍：
Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.
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