AN A3-PROOF OF STRUCTURE THEOREMS FOR CHEVALLEY GROUPS OF TYPES E6 AND E7

Abstract

In the nineties the author, A. Stepanov and E. Plotkin developed a geometric approach towards calculations in exceptional groups at the level of K 1, decomposition of unipotents. However, it relied on the presence of large classical embeddings, such as A 5 ≤ E 6 or A 7 ≤ E 7. Recently the author, M. Gavrilovich and S. Nikolenko devised a sharper geometric method which only uses embeddings A 2 ≤ E 6, E 7, F 4. Here we show that one can make a further step and simultaneously stabilize two columns of a root unipotent by an element of type A 3 ≤ E 6, E 7. This opens the way to applications of this method at the level of K 2.