Let G and E stand for one of the following pairs of groups: • Either G is the general quadratic group U(2n, R,Λ), n ≥ 3, and E its elementary subgroup EU(2n, R,Λ), for an almost commutative form ring (R,Λ), • or G is the Chevalley group G(Φ, R) of type Φ, and E its elementary subgroup E(Φ, R), where Φ is a reduced irreducible root system of rank ≥ 2 and R is commutative. Using Bak’s localizatio...

The É. Cartan’s equations defining “simple” spinors (renamed “pure” by C. Chevalley) are interpreted as equations of motions for fermion multiplets in momentum spaces which, in a constructive approach based bilinearly on those spinors, result compact and Lorentzian, naturally ending up with a ten-dimension space. The equations found are most of those traditionally adopted ad hoc by theoretical ...