On pairs of root groups and reflections associated to the Chevalley group E 6(K), in characteristic two

Abstract

This paper is concerned with computing the number of orbits under the action of the algebraic group E = E 6 ( K ) on the set of all pairs of root subgroups of itself. Furthermore, the number of orbits of the action of the group generated by a pair of certain reflections, on the 27 dimensional module A, has been computed. For the computations done in this paper, an explicit representation of E inside GL ( A ) has been fixed right at the onset.