A third look at weight diagrams
The author describes how one may compute in the Chevalley groups of type \(E_6\) or \(E_7\) (over a commutative ring) in terms of the weight diagram of a certain fundamental representation. His analysis includes signs of structure constants and signs of the terms in the quadrics that cut out the orbit of a highest weight vector. The story culminates in the `decomposition of unipotents', which is needed to prove the main structure theorems (description of normal subgroups, standard commutator formulae and the like). As is his want, the author provides a lot of background.
scientific article; zbMATH DE number 1898319
scientific article