On involutions in the Weyl group and B-orbit closures in the orthogonal case

2018/10/04 by Ignatyev, Mikhail V.
#17B08 #17B22 #17B30 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1810.02703

Abstract

We study coadjoint B-orbits on \mathfrakn^*, where B is a Borel subgroup of a complex orthogonal group G, and \mathfrakn is the Lie algebra of the unipotent radical of B. To each basis involution w in the Weyl group W of G one can assign the associated B-orbit Ω_w. We prove that, given basis involutions σ, τ in W, if the orbit Ω_σ is contained in the closure of the orbit Ω_τ then σ is less than or equal to τ with respect to the Bruhat order on W. For a basis involution w, we also compute the dimension of Ω_w and present a conjectural description of the closure of Ω_w.

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