The Bruhat−Chevalley Order on Involutions of the Hyperoctahedral Group and the Combinatorics of B-Orbit Closures
Let G = Sp2n (ℂ) be the symplectic group, B be its Borel subgroup, and Φ = Cn be the root system of G. To each involution σ in the Weyl group W of Φ, one can assign an orbit Ωσ of the coadjoint action of B on the dual space of the Lie algebra of the unipotent radical of B. Let σ, τ be involutions in W. It is proved that Ωσ is contained in the closure of Ωτ if and only if σ is less than or equal to τ with respect to the Bruhat–Chevalley order on W. Bibliography: 15 titles.