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Zap. Nauchn. Sem. POMI, 2006, Volume 338, Pages 98–124 (Mi znsl167)  

This article is cited in 3 scientific papers (total in 3 papers)

Orbits of subsystem stabilisers

N. A. Vavilov, N. P. Kharchev

Saint-Petersburg State University

Abstract: Let $\Phi$ be a reduced irreducible root system. We consider pairs $(S,X(S))$, where $S$ is a closed set of roots, $X(S)$ is its stabiliser in the Weyl group $W(\Phi)$. We are interested in such pairs maximal with respct to the following order: $(S_1,X(S_1))\le (S_2,X(S_2))$ if $S_1\subseteq S_2$ and $X(S_1)\le X(S_2)$. Main theorem asserts that if $\Delta$ is a root subsystem such that $(\Delta,X(\Delta))$ is maximal with respect to the above order, then $X(\Delta)$ acts transitively both on the long and short roots in $\Phi\setminus\Delta$. This result is a broad generalisation of the transitivity of the Weyl group on roots of given length.

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English version:
Journal of Mathematical Sciences (New York), 2007, 145:1, 4751–4764

Bibliographic databases:

UDC: 512.5
Received: 30.10.2006

Citation: N. A. Vavilov, N. P. Kharchev, “Orbits of subsystem stabilisers”, Problems in the theory of representations of algebras and groups. Part 14, Zap. Nauchn. Sem. POMI, 338, POMI, St. Petersburg, 2006, 98–124; J. Math. Sci. (N. Y.), 145:1 (2007), 4751–4764

Citation in format AMSBIB
\Bibitem{VavKha06}
\by N.~A.~Vavilov, N.~P.~Kharchev
\paper Orbits of subsystem stabilisers
\inbook Problems in the theory of representations of algebras and groups. Part~14
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 338
\pages 98--124
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl167}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2354608}
\zmath{https://zbmath.org/?q=an:1144.20023}
\elib{http://elibrary.ru/item.asp?id=9305289}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 145
\issue 1
\pages 4751--4764
\crossref{https://doi.org/10.1007/s10958-007-0306-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547515104}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Vavilov, “Numerologiya kvadratnykh uravnenii”, Algebra i analiz, 20:5 (2008), 9–40  mathnet  mathscinet  zmath; N. A. Vavilov, “Numerology of square equations”, St. Petersburg Math. J., 20:5 (2009), 687–707  crossref  isi
    2. N. A. Vavilov, “Some more exceptional numerology”, J. Math. Sci. (N. Y.), 171:3 (2010), 317–321  mathnet  crossref
    3. N. A. Vavilov, A. V. Schegolev, “Nadgruppy subsystem subgroups v isklyuchitelnykh gruppakh: urovni”, Voprosy teorii predstavlenii algebr i grupp. 23, Zap. nauchn. sem. POMI, 400, POMI, SPb., 2012, 70–126  mathnet  mathscinet; N. A. Vavilov, A. V. Shchegolev, “Overgroups of subsystem subgroups in exceptional groups: levels”, J. Math. Sci. (N. Y.), 192:2 (2013), 164–195  crossref
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