Which Schubert Varieties are Hessenberg Varieties?
Laura Escobar, Martha Precup, John Shareshian

TL;DR
This paper proves that all Schubert varieties in the full flag variety are Hessenberg varieties but not all are adjoint Hessenberg varieties, especially in types A and C, with many not being isomorphic to any.
Contribution
It establishes that every Schubert variety is a general Hessenberg variety and provides criteria showing most are not adjoint Hessenberg varieties in certain types.
Findings
All Schubert varieties are general Hessenberg varieties.
Most Schubert varieties in types A and C are not adjoint Hessenberg varieties.
Some Schubert varieties in type A are not isomorphic to any adjoint Hessenberg variety.
Abstract
After proving that every Schubert variety in the full flag variety of a complex reductive group 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 increases. We show also that in type A, some Schubert varieties are not isomorphic to any adjoint Hessenberg variety.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models
