Abstract:
The article is dedicated to description of overgroups of elementary Chevalley groups of types E6 and E7 in their minimal irreducible representations. One of the first step towards such description, namely construction of the series of perfect intermediate groups, is made. Probably all perfect intermediate groups for groups of type E6 are described. The hypothesis concerning the structure of perfect overgroups of type E7 is made.
Citation:
A. Yu. Luzgarev, “On overgroups of E(E6,R) and E(E7,R) in their
minimal representations”, Problems in the theory of representations of algebras and groups. Part 11, Zap. Nauchn. Sem. POMI, 319, POMI, St. Petersburg, 2004, 216–243; J. Math. Sci. (N. Y.), 134:6 (2006), 2558–2571
\Bibitem{Luz04}
\by A.~Yu.~Luzgarev
\paper On overgroups of $\mathrm{E}(\mathrm{E}_6,R)$ and $\mathrm{E}(\mathrm{E}_7,R)$ in their
minimal representations
\inbook Problems in the theory of representations of algebras and groups. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 319
\pages 216--243
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl614}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2117858}
\zmath{https://zbmath.org/?q=an:1104.20050}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 134
\issue 6
\pages 2558--2571
\crossref{https://doi.org/10.1007/s10958-006-0127-5}
Linking options:
https://www.mathnet.ru/eng/znsl614
https://www.mathnet.ru/eng/znsl/v319/p216
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