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 Zap. Nauchn. Sem. POMI, 1999, Volume 265, Pages 42–63 (Mi znsl1189)

Subgroups of the split orthogonal group. II

N. A. Vavilov

Saint-Petersburg State University

Abstract: In the first paper of the series, we proved standardness of subgroups containing a split maximal torus in the split orthogonal group $SO(n,R)$ over a commutative semilocal ring $R$ for the two following situations: 1) $n$ is even, 2) $n$ is odd and $R=K$ is a field. In the present paper we prove standardness of intermediate subgroups over a semilocal ring $R$ in the case of an odd $n$. Together with the preceeding papers by Z. I. Borewicz, the author, and E. V. Dybkova this paper completes description of the overgroups of split maximal tori in the classical groups over semilocal rings. The analysis of odd orthogonal groups turned out to be technically much more difficult than other classical cases. Unlike all preceeding papers the proof of the key step in the reduction to the field case relies on calculations with a class of semisimple elements which are neither microweight elements, nor semisimple root elements.

Full text: PDF file (272 kB)

English version:
Journal of Mathematical Sciences (New York), 2002, 112:3, 4266–4276

Bibliographic databases:

UDC: 519.46

Citation: N. A. Vavilov, “Subgroups of the split orthogonal group. II”, Problems in the theory of representations of algebras and groups. Part 6, Zap. Nauchn. Sem. POMI, 265, POMI, St. Petersburg, 1999, 42–63; J. Math. Sci. (New York), 112:3 (2002), 4266–4276

Citation in format AMSBIB
\Bibitem{Vav99} \by N.~A.~Vavilov \paper Subgroups of the split orthogonal group.~II \inbook Problems in the theory of representations of algebras and groups. Part~6 \serial Zap. Nauchn. Sem. POMI \yr 1999 \vol 265 \pages 42--63 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl1189} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1757815} \zmath{https://zbmath.org/?q=an:1052.20030} \transl \jour J. Math. Sci. (New York) \yr 2002 \vol 112 \issue 3 \pages 4266--4276 \crossref{https://doi.org/10.1023/A:1020378516076} 

• http://mi.mathnet.ru/eng/znsl1189
• http://mi.mathnet.ru/eng/znsl/v265/p42

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. A. Vavilov, V. A. Petrov, “Overgroups of $\mathrm{EO}(n,R)$”, St. Petersburg Math. J., 19:2 (2008), 167–195
2. N. A. Vavilov, “On subgroups of symplectic group containing a subsystem subgroup”, J. Math. Sci. (N. Y.), 151:3 (2008), 2937–2948
3. N. A. Vavilov, “Subgroups of $\operatorname{SL}_n$ over a semilocal ring”, J. Math. Sci. (N. Y.), 147:5 (2007), 6995–7004