  In a space of $d $ Grassmann coordinates two types of generators of Lorentz
transformations can be defined, one of spinorial and the other of vectorial
character. Both kinds of operators appear as linear operators in Grassmann
space, definig the fundamental and the adjoint representations of the group $
SO(1,d$$-$$1) $, respectively. The eigenvalues of commuting operators belonging
to the subgroup $(SO(1,4)) $ can be identified with spins of either fermionic
or bosonic fields, while the operators belonging to subgroups of $ SO(d$$-$$5)
$ ${\supset SU(3)}$ $ {\times SU(2)}$ $ {\times U(1)} $, determine the
Yang-Mills charges. The theory offers unification of all the internal degrees
of freedom of fermionic and bosonic fields - spins and all Yang-Mills charges.
When accordingly all interactions are unified, Yang-Mills fields appear as part
of the gravitational field. The theory suggests that elementary particles are
either in the fundamental representations with respect to the groups
determining the spin and the charges, or they are in the adjoint
representations with respect to the groups, which determine the spin and the
charges.
