The purpose of the paper is to determine all cases in which the dual variety is not of codimension one. When *G* is simple there are the following cases (upto isomorphims of *G* and *V*):

*G*=SL(*n*,*k*), *V*=*k ^{n}*;

The classification for semisimple groups is easily obtained from that.}, author = {Knop, Friedrich and Menzel, Gisela}, doi = {10.5169/seals-47339}, faupublication = {no}, journal = {Commentarii Mathematici Helvetici}, month = {Jan}, pages = {38-61}, peerreviewed = {Yes}, title = {{Duale} {VarietÃ¤ten} von {FahnenvarietÃ¤ten}}, volume = {62}, year = {1987} }