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- W3042051288 abstract "Flag varieties are well-known algebraic varieties with many important geometric, combinatorial, and representation theoretic properties. A Hessenberg variety is a subvariety of a flag variety identified by two parameters: an element (X) of the Lie algebra (mathfrak{g}) and a Hessenberg subspace (Hsubseteq mathfrak{g}). This paper considers when two Hessenberg spaces define the same Hessenberg variety when paired with (X). To answer this question we present the containment poset (mathcal{P}_X) of type (A) Hessenberg varieties with a fixed first parameter (X) and give a simple and elegant proof that if (X) is not a multiple of the element (bf 1) then the Hessenberg spaces containing the Borel subalgebra determine distinct Hessenberg varieties. Lastly we give a natural involution on (mathcal{P}_X) that induces a homeomorphism of varieties and prove additional properties of (mathcal{P}_X) when (X) is a regular nilpotent element." @default.
- W3042051288 created "2020-07-16" @default.
- W3042051288 creator A5062658510 @default.
- W3042051288 date "2020-01-01" @default.
- W3042051288 modified "2023-09-24" @default.
- W3042051288 title "The containment poset of type A Hessenberg varieties" @default.
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- W3042051288 doi "https://doi.org/10.12958/adm1216" @default.
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