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Towards the Reverse Decomposition of Unipotents

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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 the 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 generalizations of these results for exceptional groups, specifically those of types E6 and E7, and also mention further possible generalizations and applications.

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  1. St. Petersburg State University, St. Petersburg, Russia

    N. A. Vavilov

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Jesus said to them, “Have you never read in the Scriptures: “The stone that the builders rejected has become the cornerstone”; this was the Lord’s doing, and it is marvelous in our eyes.”

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 470, 2018, pp. 21–37.

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Vavilov, N.A. Towards the Reverse Decomposition of Unipotents. J Math Sci 243, 515–526 (2019). https://doi.org/10.1007/s10958-019-04553-x

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