Geometry of root elements in groups of type 𝐸₆

Pevzner, I.

doi:10.1090/S1061-0022-2012-01210-0

Geometry of root elements in groups of type ${\mathrm E}_{6}$
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by I. M. Pevzner
Translated by: A. Luzgarev

St. Petersburg Math. J. 23 (2012), 603-635

DOI: https://doi.org/10.1090/S1061-0022-2012-01210-0

Published electronically: March 2, 2012

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Abstract:

Root elements in the 27-dimensional representation of the simply connected Chevalley group of type $\mathrm E_7$ over a field are studied. With every root subgroup, a certain six-dimensional singular subspace is associated; this correspondence is shown to be a natural bijection. Also, the notion of the angle between root subgroups is described in terms of singular subspaces.

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