Partial order on involutive permutations and double Schubert cells

2024/05/14 by Evgeny Smirnov, Smirnov, Evgeny
Mathematics · #05E10 (Primary) 14M15 #14M27 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2405.08646

openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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