Complex hidden symmetries in real spacetime and their algebraic structures

Considering real spacetime as a Lorentzian fiber in a complex manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincar\'{e} groups. No spinors are allowed as linear irreducible representations for the complex case, but when a spin$^{h}$ structure is implemented on the associated principal bundles, one is naturally led to an algebraic structure similar to the one of the standard model. This last (dynamical) structure might therefore be inherited from the kinematical symmetries of a larger space.