, Volume 42, Issue 3, pp 341-344

A linear interpretation of the flag geometries of Chevalley groups

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Abstract

It is proven that the flag geometry of a Chevalley group can be derived from the flag geometry of its Weyl group by using a linear covering defined by the author. To prove this, the author regards elements of the Weyl group geometry as vectors of a Euclidean space in such a way that the incidence of vectors is defined by their scalar products.

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 383–387, March, 1990.