Subgroups of the spinor group containing a split maximal torus.~II
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 37-56
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In the first paper of the series, we proved standardness of a subgroup $H$ containing a split maximal torus in the split spinor group $\operatorname{Spin}(n,K)$ over a field $K$ of characteristic not 2 containing at least 7 elements under one of the following additional assumptions: 1) $H$ is reducible, 2) $H$ is imprimitive, 3) $H$ contains a non-trivial root element. In the present paper we finish the proof of a result announced by the author in 1990 and prove standardness of all intermediate subgroups provided $n=2l$ and $|K|\ge9$. For an algebraically closed $K$ this follows from a classical result of Borel and Tits and for a finite $K$ this was proven by Seitz. Similar results for subgroups of orthogonal groups $SO(n,R)$ were previously obtained by the author, not only for fields, but for any commutative semi-local ring $R$ with large enough residue fields.
@article{ZNSL_2002_289_a1,
author = {N. A. Vavilov},
title = {Subgroups of the spinor group containing a split maximal {torus.~II}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {37--56},
publisher = {mathdoc},
volume = {289},
year = {2002},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a1/}
}
N. A. Vavilov. Subgroups of the spinor group containing a split maximal torus.~II. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 37-56. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a1/