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


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Let D be a division algebra with a fixed involution, and let V be the corresponding unitary space over D with T -condition (see N. Bourbaki, Algèbre). For a pair of totally isotropic subspaces u, v ≤ V, the double cosets PuγPv of their stabilizers Pu, Pv in Γ = SU(V ) are considered. A description of the cosets PuγPv in terms of the intersection distance din(u, γ(v)) and the Witt index of u + γ(v) is given.

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N. Gordeev

St.Petersburg State University

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Email: nickgordeev@mail.ru
俄罗斯联邦, St.Petersburg

U. Rehmann

Bielefeld University

Email: nickgordeev@mail.ru
德国, Bielefeld

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