Let D be a division algebra with an involution \(\star \) and with the centre F and let V be a finite-dimensional vector space with a symmetric or skew-symmetric hermitian form. Further, let h be isotropic and let \(P_u, P_v\) be the stabilizers of totally isotropic subspaces \(u, v \leqslant V\) in the group \(\textrm{SU}\hspace{0.55542pt}(D, h)\) . In the papers [6, 7] it was considered the “geometrical” description of double cosets \(P_u g P_v\) where \(g \in \textrm{SU}\hspace{0.55542pt}(D, h)\) . Namely, such a coset is defined uniquely by the dimension and the Witt index of the space \(u + g(v)\) (with one exception). The “adherence” of double cosets is also defined by geometrical parameters. It has been proved for the case when \(\star \) is an involution of the first kind (that is, \(\star \) acts trivially on F). In this paper we give the same description of adherence for the cases of involutions of the second kind.
