Double Cosets of Stabilizers of Totally Isotropic Subspaces in a Special Unitary Group II
- Authors: Gordeev N.1,2, Rehmann U.3
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Affiliations:
- Russian State Pedagogical University
- St. Petersburg State University
- Bielefeld University
- Issue: Vol 240, No 4 (2019)
- Pages: 428-446
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242758
- DOI: https://doi.org/10.1007/s10958-019-04361-3
- ID: 242758
Cite item
Abstract
In 2016, the authors considered the decomposition \( \mathrm{SU}\left(D,h\right)=\underset{i}{\cup }{P}_u{\gamma}_i{P}_{\upsilon } \), 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 Pu, Pυ are stabilizers of totally isotropic subspaces of the unitary space. Since Γ = SU(D, h) is a point group of a classical algebraic group \( \tilde{\Gamma} \), there is the “order of adherence” on the set of double cosets {PuγiPυ}, which is induced by the Zariski topology on \( \tilde{\Gamma} \). In the present paper, the adherence of such double cosets is described for the cases where \( \tilde{\Gamma} \) is an orthogonal or a symplectic group (that is, for groups of types Br, Cr, Dr).
About the authors
N. Gordeev
Russian State Pedagogical University; St. Petersburg State University
Author for correspondence.
Email: nickgordeev@mail.ru
Russian Federation, St. Petersburg; St. Petersburg
U. Rehmann
Bielefeld University
Email: nickgordeev@mail.ru
Germany, Bielefeld