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arXiv · 2107.07929

Which Schubert Varieties are Hessenberg Varieties?

Laura Escobar·Martha Precup·John Shareshian
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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.

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Laura Escobar, Martha Precup, John Shareshian. 2021-07-16. Which Schubert Varieties are Hessenberg Varieties?. https://arxiv.org/abs/2107.07929

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