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

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.

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

Bibliographic databases:

UDC: 512.5+512.6+512.7+512.8

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} 

• http://mi.mathnet.ru/eng/znsl1594
• http://mi.mathnet.ru/eng/znsl/v289/p37

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This publication is cited in the following articles:
1. N. A. Vavilov, “On subgroups of symplectic group containing a subsystem subgroup”, J. Math. Sci. (N. Y.), 151:3 (2008), 2937–2948
2. N. A. Vavilov, “Subgroups of $\operatorname{SL}_n$ over a semilocal ring”, J. Math. Sci. (N. Y.), 147:5 (2007), 6995–7004