  A generalized vector particle theory with the use of an extended set of
Lorentz group irredicible representations, including scalar, two 4-vectors, and
antisymmetric 2-rang tensor, is investigated. Initial equations depend upon
four complex parameters $\lambda_{i}$, obeying two supplementary conditions, so
restriction of the model to the case of electrically neutral vector particle is
not a trivial task. A special basis in the space of 15-component wave functions
is found where instead of four $\lambda_{i}$ only one real-valued quantity
$\sigma$, a bilinear combination of $\lambda_{i}$, is presented. This
$\lambda$-parameter is interpreted as an additional electromagnetic
characteristic of a charged vector particle, polarizability. It is shown that
in this basis $C$-operation is reduced to the complex conjugation only, without
any accompanying linear transformation. Restriction to a massless vector
particle is determined.
  Extension of the whole theory to the case of Riemannian space-time is
accomplished. Two methods of obtaining corresponding generally covariant wave
equations are elaborated: of tensor- and of tetrad-based ones. Their
equivalence is proved. It is shown that in case of pure curved space-time
models without Cartan torsion no specific additional interaction terms because
of non-flat geometry arise. The conformal symmetry of a massless generally
covariant equation is demonstrated explicitly. A canonical tensor of
energy-momentum $T_{\beta \alpha}$ is constructed, its conservation law happens
to involves the Riemann curvature tensor. Within the framework of known
ambiguity of any energy-momentum tensor, a new tensor $\bar{T}_{\beta \alpha}$
is suggested to be used, which obeys a common conservation law.
