Partial order on involutive permutations and double Schubert cells
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911876726652928 |
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| author | Smirnov, Evgeny |
| author_facet | Smirnov, Evgeny |
| contents | As shown by A. Melnikov, the orbits of a Borel subgroup acting by conjugation on upper-triangular matrices with square zero are indexed by involutions in the symmetric group. The inclusion relation among the orbit closures defines a partial order on involutions. We observe that the same order on involutive permutations also arises while describing the inclusion order on B-orbit closures in the direct product of two Grassmannians. We establish a geometric relation between these two settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial order on involutive permutations and double Schubert cells Smirnov, Evgeny Combinatorics 05E10 (Primary) 14M15, 14M27 (Secondary) As shown by A. Melnikov, the orbits of a Borel subgroup acting by conjugation on upper-triangular matrices with square zero are indexed by involutions in the symmetric group. The inclusion relation among the orbit closures defines a partial order on involutions. We observe that the same order on involutive permutations also arises while describing the inclusion order on B-orbit closures in the direct product of two Grassmannians. We establish a geometric relation between these two settings. |
| title | Partial order on involutive permutations and double Schubert cells |
| topic | Combinatorics 05E10 (Primary) 14M15, 14M27 (Secondary) |
| url | https://arxiv.org/abs/2405.08646 |