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

  • N. GordeevEmail author
  • U. Rehmann
Article

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).

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Russian State Pedagogical UniversitySt. PetersburgRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia
  3. 3.Bielefeld UniversityBielefeldGermany

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