Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties
| Autor: | Harada, Megumi, Precup, Martha |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | It is well-known that the $T$-fixed points of a Schubert variety in the flag variety $GL_n(\mathbb{C})/B$ can be characterized purely combinatorially in terms of Bruhat order on the symmetric group $\mathfrak{S}_n$. In a recent preprint, Cho, Hong, and Lee give a combinatorial description of the $T$-fixed points of Hessenberg analogues of Schubert varieties (which we call Hessenberg Schubert varieties) in a regular semisimple Hessenberg variety. This note gives an interpretation of their result in terms of Bruhat order by making use of a partition of the symmetric group defined using so-called subsets of Weyl type. The Appendix, written by Michael Zeng, proves a lemma concerning subsets of Weyl type which is required in our arguments. Comment: 13 pages. Major revision, due to an error discovered in the proof of the main theorem of the previous version. The current version states and proves a revised result, which concerns the T-fixed points of the Hessenberg Schubert variety instead of the variety itself |
| Databáze: | arXiv |
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