The containment poset of type A Hessenberg varieties
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 g and a Hessenberg subspace H ⊆ g. This paper...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188515 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The containment poset of type A Hessenberg varieties / E. Drellich // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 2. — С. 195–210. — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725747747061760 |
|---|---|
| author | Drellich, E. |
| author_facet | Drellich, E. |
| citation_txt | The containment poset of type A Hessenberg varieties / E. Drellich // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 2. — С. 195–210. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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 g and a Hessenberg subspace H ⊆ 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 Px 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 1 then the Hessenberg spaces containing the Borel subalgebra determine distinct Hessenberg varieties. Lastly we give a natural involution on Px that induces a homeomorphism of varieties and prove additional properties of Px when X is a regular nilpotent element.
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| first_indexed | 2025-12-07T18:53:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188515 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:53:47Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Drellich, E. 2023-03-03T19:39:04Z 2023-03-03T19:39:04Z 2020 The containment poset of type A Hessenberg varieties / E. Drellich // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 2. — С. 195–210. — Бібліогр.: 15 назв. — англ. 1726-3255 DOI:10.12958/adm1216 2010 MSC: 14A25, 17B45, 05E99. https://nasplib.isofts.kiev.ua/handle/123456789/188515 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 g and a Hessenberg subspace H ⊆ 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 Px 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 1 then the Hessenberg spaces containing the Borel subalgebra determine distinct Hessenberg varieties. Lastly we give a natural involution on Px that induces a homeomorphism of varieties and prove additional properties of Px when X is a regular nilpotent element. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics The containment poset of type A Hessenberg varieties Article published earlier |
| spellingShingle | The containment poset of type A Hessenberg varieties Drellich, E. |
| title | The containment poset of type A Hessenberg varieties |
| title_full | The containment poset of type A Hessenberg varieties |
| title_fullStr | The containment poset of type A Hessenberg varieties |
| title_full_unstemmed | The containment poset of type A Hessenberg varieties |
| title_short | The containment poset of type A Hessenberg varieties |
| title_sort | containment poset of type a hessenberg varieties |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188515 |
| work_keys_str_mv | AT drelliche thecontainmentposetoftypeahessenbergvarieties AT drelliche containmentposetoftypeahessenbergvarieties |