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arXiv · 2405.08646

Partial order on involutive permutations and double Schubert cells

Evgeny Smirnov
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Abstract

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.

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Evgeny Smirnov. 2024-05-14. Partial order on involutive permutations and double Schubert cells. https://arxiv.org/abs/2405.08646

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