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 Zap. Nauchn. Sem. POMI, 2017, Volume 460, Pages 82–113 (Mi znsl6472)

Double cosets of stabilizers of totally isotropic subspaces in a special unitary group II

N. Gordeevab, U. Rehmannc

a Department of Mathematics, Russian State Pedagogical University, Moijka 48, St. Petersburg, 191186, Russia
b St. Petersburg State University, Universitetsky prospekt, 28, Peterhof, St. Petersburg, 198504, Russia
c Department of Mathematics, Bielefeld University, Universitätsstrasse 25, D-33615 Bielefeld, Germany

Abstract: In the article (N. Gordeev and U. Rehmann. Double cosets of stabilizers of totally isotropic subspaces in a special unitary group I, Zapiski Nauch. Sem. POMI, v. 452 (2016), 86–107) we have considered the decomposition $\mathrm{SU}(D,h)=\cup_iP_u\gamma_iP_v$ where $\mathrm{SU}(D,h)$ is a special unitary group over a division algebra $D$ with an involution, $h$ is a symmetric or skew symmetric non-degenerated Hermitian form, and $P_u,P_v$ are stabilizers of totally isotropic subspaces of the unitary space. Since $\Gamma=\mathrm{SU}(D,h)$ is a point group of a classical algebraic group $\widetilde\Gamma$ there is the “order of adherence” on the set of double cosets $\{P_u\gamma_iP_v\}$ which is induced by the Zariski topology on $\Gamma$. In the current paper we describe the adherence of such double cosets for the cases when $\widetilde\Gamma$ is an orthogonal or a symplectic group (that is, for groups of types $B_r,C_r,D_r$).

Key words and phrases: classical algebraic groups, double cosets of closed subgroups, the order of adherence.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.661.2016/1.4 The first author is supported by the Ministry of Science and Education of the Russian Federation, grant number 1.661.2016/1.4.

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English version:
Journal of Mathematical Sciences (New York), 2019, 240:4, 428–446

UDC: 512.7+512.81
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Citation: N. Gordeev, U. Rehmann, “Double cosets of stabilizers of totally isotropic subspaces in a special unitary group II”, Problems in the theory of representations of algebras and groups. Part 32, Zap. Nauchn. Sem. POMI, 460, POMI, St. Petersburg, 2017, 82–113; J. Math. Sci. (N. Y.), 240:4 (2019), 428–446

Citation in format AMSBIB
\Bibitem{GorReh17} \by N.~Gordeev, U.~Rehmann \paper Double cosets of stabilizers of totally isotropic subspaces in a~special unitary group~II \inbook Problems in the theory of representations of algebras and groups. Part~32 \serial Zap. Nauchn. Sem. POMI \yr 2017 \vol 460 \pages 82--113 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6472} \transl \jour J. Math. Sci. (N. Y.) \yr 2019 \vol 240 \issue 4 \pages 428--446 \crossref{https://doi.org/10.1007/s10958-019-04361-3}