  Contemporary presentation of the version 1 demonstrates briefly the
development of our investigations and our future goals. The improved free of
difficulties in interpretation and printing errors version is presented. The
256-dimensional gamma matrix representations of the Clifford algebra and
corresponding representations of SO(10) and SO(1,9) algebras over the field of
real numbers are introduced. This turned out to be possible in the space of
eight-component spinors, and not for the ordinary four-component Dirac spinors.
The proposed mathematical objects allow the generalization of our results,
obtained earlier for the standard Dirac equation, for the equations of higher
spin and, especially, for the equations, describing the particles with spin
3/2.
