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Zap. Nauchn. Sem. POMI, 2002, Volume 289, Pages 37–56 (Mi znsl1594)  

This article is cited in 2 scientific papers (total in 2 papers)

Subgroups of the spinor group containing a split maximal torus. II

N. A. Vavilov

Saint-Petersburg State University

Abstract: In the first paper of the series, we proved standardness of a subgroup $H$ containing a split maximal torus in the split spinor group $\operatorname{Spin}(n,K)$ over a field $K$ of characteristic not 2 containing at least 7 elements under one of the following additional assumptions: 1) $H$ is reducible, 2) $H$ is imprimitive, 3) $H$ contains a non-trivial root element. In the present paper we finish the proof of a result announced by the author in 1990 and prove standardness of all intermediate subgroups provided $n=2l$ and $|K|\ge9$. For an algebraically closed $K$ this follows from a classical result of Borel and Tits and for a finite $K$ this was proven by Seitz. Similar results for subgroups of orthogonal groups $SO(n,R)$ were previously obtained by the author, not only for fields, but for any commutative semi-local ring $R$ with large enough residue fields.

Full text: PDF file (266 kB)

English version:
Journal of Mathematical Sciences (New York), 2004, 124:1, 4698–4707

Bibliographic databases:

UDC: 512.5+512.6+512.7+512.8
Received: 10.06.2001

Citation: N. A. Vavilov, “Subgroups of the spinor group containing a split maximal torus. II”, Problems in the theory of representations of algebras and groups. Part 9, Zap. Nauchn. Sem. POMI, 289, POMI, St. Petersburg, 2002, 37–56; J. Math. Sci. (N. Y.), 124:1 (2004), 4698–4707

Citation in format AMSBIB
\Bibitem{Vav02}
\by N.~A.~Vavilov
\paper Subgroups of the spinor group containing a split maximal torus.~II
\inbook Problems in the theory of representations of algebras and groups. Part~9
\serial Zap. Nauchn. Sem. POMI
\yr 2002
\vol 289
\pages 37--56
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1594}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1949732}
\zmath{https://zbmath.org/?q=an:1070.20057}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 124
\issue 1
\pages 4698--4707
\crossref{https://doi.org/10.1023/B:JOTH.0000042305.51231.e8}


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    This publication is cited in the following articles:
    1. N. A. Vavilov, “O podgruppakh simplekticheskoi gruppy, soderzhaschikh subsystem subgroup”, Voprosy teorii predstavlenii algebr i grupp. 16, Zap. nauchn. sem. POMI, 349, POMI, SPb., 2007, 5–29  mathnet  mathscinet  elib; N. A. Vavilov, “On subgroups of symplectic group containing a subsystem subgroup”, J. Math. Sci. (N. Y.), 151:3 (2008), 2937–2948  crossref  elib
    2. N. A. Vavilov, “Subgroups of $\operatorname{SL}_n$ over a semilocal ring”, J. Math. Sci. (N. Y.), 147:5 (2007), 6995–7004  mathnet  crossref  mathscinet  elib  elib
  • Записки научных семинаров ПОМИ
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