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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 452, Pages 86–107 (Mi znsl6358)  
This article is cited in 2 scientific papers (total in 2 papers)

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

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 Ulf Rehmann, Department of Mathematics, Bielefeled University, Universitätsstrasse 25, D-33615 Bielefeld, Germany
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Abstract: Let $D$ be a division algebra with a fixed involution and let $V$ be the corresponding unitary space over $D$ with $T$-condition (see [2]). For a pair of totally isotropic subspaces $u,v\leq V$ we consider the double cosets $P_u\gamma P_v$ of their stabilizers $P_u,P_v$ in $\Gamma=\mathrm{SU}(V)$. We give a description of cosets $P_u\gamma P_v$ in the terms of the intersection distance $d_\mathrm{in}(u,\gamma(v))$ and the Witt index of $u+\gamma(v)$.
Key words and phrases: classical algebraic groups, double cosets of closed subgroups, intersection distance.
Received: 22.09.2016
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 232, Issue 5, Pages 647–661
DOI: https://doi.org/10.1007/s10958-018-3895-9
Bibliographic databases:
Document Type: Article
UDC: 512.74
Language: English
Citation: N. Gordeev, U. Rehmann, “Double cosets of stabilizers of totally isotropic subspaces in a special unitary group I”, Problems in the theory of representations of algebras and groups. Part 30, Zap. Nauchn. Sem. POMI, 452, POMI, St. Petersburg, 2016, 86–107; J. Math. Sci. (N. Y.), 232:5 (2018), 647–661
Citation in format AMSBIB
\Bibitem{GorReh16}
\by N.~Gordeev, U.~Rehmann
\paper Double cosets of stabilizers of totally isotropic subspaces in a~special unitary group~I
\inbook Problems in the theory of representations of algebras and groups. Part~30
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 452
\pages 86--107
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6358}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3589285}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 232
\issue 5
\pages 647--661
\crossref{https://doi.org/10.1007/s10958-018-3895-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048505512}
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