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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 522, Pages 101–112 (Mi znsl7338)  

Extraction of small rank unipotent elements in $\mathrm{SO}(2\ell,K)$

V. V. Nesterov

Saint Petersburg State University
References:
Abstract: The paper continues the series of papers of N.A. Vavilov and the author devoted to the geometry of microweight tori in extended Chevalley groups. It is proved that the subgroup, generated by a pair of microweight tori of type $\bar\omega_1$ in a Chevalley group of type $\mathrm{D}_\ell$, contains unipotent elements of rank less than or equal to 4 provided that the field has at least 19 elements. These unipotent elements are either a root unipotent element or the product of two root unipotent elements corresponding to orthogonal roots.
Key words and phrases: Chevalley groups, orthogonal groups, microweight tori, unipotents elements.
Received: 05.06.2023
Document Type: Article
UDC: 512.542.6
Language: Russian
Citation: V. V. Nesterov, “Extraction of small rank unipotent elements in $\mathrm{SO}(2\ell,K)$”, Problems in the theory of representations of algebras and groups. Part 39, Zap. Nauchn. Sem. POMI, 522, POMI, St. Petersburg, 2023, 101–112
Citation in format AMSBIB
\Bibitem{Nes23}
\by V.~V.~Nesterov
\paper Extraction of small rank unipotent elements in $\mathrm{SO}(2\ell,K)$
\inbook Problems in the theory of representations of algebras and groups. Part~39
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 522
\pages 101--112
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7338}
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