Séminaire Lotharingien de Combinatoire, 93B.30 (2025), 12 pp.
Evgeny Smirnov
Partial Order on Involutive Permutations and B-Orbit Closures in Double Grassmannians
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.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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