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

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 P u γP v of their stabilizers P u , P v in Γ = SU( V ) are considered. A desc...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2018-08, Vol.232 (5), p.647-661
Main Authors: Gordeev, N., Rehmann, U.
Format: Article
Language:English
Subjects:
ALGEBRA
DISTANCE
ISOTROPY
MATHEMATICAL METHODS AND COMPUTING
MATHEMATICAL SPACE
Mathematics
Mathematics and Statistics
Subspaces
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Summary: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 P u γP v of their stabilizers P u , P v in Γ = SU( V ) are considered. A description of the cosets P u γP v in terms of the intersection distance d in ( u, γ ( v )) and the Witt index of u + γ ( v ) is given.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-3895-9