哪些舒伯特品种是海森伯格品种?

Pub Date : 2023-11-18 DOI:10.1007/s00031-023-09825-0

Laura Escobar, Martha Precup, John Shareshian

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引用次数: 3

摘要

在证明复约群G的满旗变种中的每一个Schubert变种都是一般的Hessenberg变种之后，我们证明了并非所有这样的Schubert变种都是伴随Hessenberg变种。事实上，在A和C类型中，我们提供了模式回避准则，暗示随着G的增加，Schubert品种是伴随的Hessenberg品种的比例趋于零。我们还证明了在A型中，一些Schubert变种与任何伴随的Hessenberg变种不同构。

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Which Schubert Varieties are Hessenberg Varieties?

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.

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