Reduction theorems for triples of short root subgroups in Chevalley groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 106-132
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In the present paper we prove the reduction theorems for triple short root unipotent subgroups in Chevalley groups of type $\mathrm B_\ell$ and $\mathrm C_\ell$. The main result roughly speaking is the following. Any subgroup generated by a triple of subgroups in question (apart from one case) is conjugate to a subgroup of
$$
G(\mathrm B_4,K)U(\mathrm B_5,K)\quad\mathrm{or}\quad G(\mathrm C_4,K)U(\mathrm C_5,K),
$$
respectively.
@article{ZNSL_2016_443_a9,
author = {V. V. Nesterov},
title = {Reduction theorems for triples of short root subgroups in {Chevalley} groups},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {106--132},
publisher = {mathdoc},
volume = {443},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a9/}
}
V. V. Nesterov. Reduction theorems for triples of short root subgroups in Chevalley groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 106-132. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a9/