  Spinor structure and internal symmetries are considered within one
theoretical framework based on the generalized spin and abstract Hilbert space.
Complex momentum is understood as a generating kernel of the underlying spinor
structure. It is shown that tensor products of biquaternion algebras are
associated with the each irreducible representation of the Lorentz group.
Space-time discrete symmetries $P$, $T$ and their combination $PT$ are
generated by the fundamental automorphisms of this algebraic background
(Clifford algebras). Charge conjugation $C$ is presented by a
pseudoautomorphism of the complex Clifford algebra. This description of the
operation $C$ allows one to distinguish charged and neutral particles including
particle-antiparticle interchange and truly neutral particles. Spin and charge
multiplets, based on the interlocking representations of the Lorentz group, are
introduced. A central point of the work is a correspondence between Wigner
definition of elementary particle as an irreducible representation of the
Poincar\'{e} group and $SU(3)$-description (quark scheme) of the particle as a
vector of the supermultiplet (irreducible representation of $SU(3)$). This
correspondence is realized on the ground of a spin-charge Hilbert space. Basic
hadron supermultiplets of $SU(3)$-theory (baryon octet and two meson octets)
are studied in this framework. It is shown that quark phenomenologies are
naturally incorporated into presented scheme. The relationship between mass and
spin is established. The introduced spin-mass formula and its combination with
Gell-Mann--Okubo mass formula allows one to take a new look at the problem of
mass spectrum of elementary particles.
