Double Cosets of Stabilizers of Totally Isotropic Subspaces in a Special Unitary Group II

In 2016, the authors considered the decomposition SU D h = ∪ i P u γ i P υ , where SU( D , h ) is a special unitary group over a division algebra D with involution, h is a symmetric or skew-symmetric nondegenerate Hermitian form, and P u , P υ are stabilizers of totally isotropic subspaces of the unitary space. Since Γ = SU( D , h ) is a point group of a classical algebraic group Γ ˜ , there is the “order of adherence” on the set of double cosets { P u γ i P υ }, which is induced by the Zariski topology on Γ ˜ . In the present paper, the adherence of such double cosets is described for the cases where Γ ˜ is an orthogonal or a symplectic group (that is, for groups of types B r , C r , D r ).