TY - JOUR

T1 - Towards the Reverse Decomposition of Unipotents

AU - Vavilov, N. A.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - исключительные группы

KW - классические группы

KW - элементарная подгруппа

KW - разложение унипотентов

KW - обратное разложение унипотентов

UR - http://www.scopus.com/inward/record.url?scp=85074857900&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04553-x

DO - 10.1007/s10958-019-04553-x

M3 - Article

AN - SCOPUS:85074857900

VL - 243

SP - 515

EP - 526

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -