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 Zap. Nauchn. Sem. POMI, 2018, Volume 470, Pages 21–37 (Mi znsl6609)

Towards the reverse decomposition of unipotents

N. A. Vavilov

St. Petersburg State University

Abstract: Decomposition of unipotents gives short polynomial expressions of the conjugates of elementary generators as products of elementaries. It turns out that with some minor twist the decomposition of unipotents can be read backwards, to give very short polynomial expressions of elementary generators themselves in terms of elementary conjugates of an arbitrary matrix and its inverse. For absolute elementary subgroups of classical groups this was recently observed by Raimund Preusser. I discuss various generalisations of these results for exceptional groups, specifically those of types $\mathrm E_6$ and $\mathrm E_7$, and also mention further possible generalisations and applications.

Key words and phrases: classical groups, Chevalley groups, normal structure, elementary subgroups, decomposition of unipotents, reverse decomposition of unipotents.

 Funding Agency Grant Number Russian Science Foundation 17-11-01261 This publication is supported by Russian Science Foundation grant 17-11-01261.

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Document Type: Article
UDC: 512.5
Language: English

Citation: N. A. Vavilov, “Towards the reverse decomposition of unipotents”, Problems in the theory of representations of algebras and groups. Part 33, Zap. Nauchn. Sem. POMI, 470, POMI, St. Petersburg, 2018, 21–37

Citation in format AMSBIB
\Bibitem{Vav18} \by N.~A.~Vavilov \paper Towards the reverse decomposition of unipotents \inbook Problems in the theory of representations of algebras and groups. Part~33 \serial Zap. Nauchn. Sem. POMI \yr 2018 \vol 470 \pages 21--37 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6609}