Geodesic
Double cosets of stabilizers of totally isotropic subspaces in a special unitary group I
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 86-107 
N. Gordeev; U. Rehmann. Double cosets of stabilizers of totally isotropic subspaces in a special unitary group I. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 86-107. http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a4/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $D$ be a division algebra with a fixed involution and let $V$ be the corresponding unitary space over $D$ with $T$-condition (see [2]). For a pair of totally isotropic subspaces $u,v\leq V$ we consider the double cosets $P_u\gamma P_v$ of their stabilizers $P_u,P_v$ in $\Gamma=\mathrm{SU}(V)$. We give a description of cosets $P_u\gamma P_v$ in the terms of the intersection distance $d_\mathrm{in}(u,\gamma(v))$ and the Witt index of $u+\gamma(v)$.

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