  In this paper, starting from pure group-theoretical point of view, we develop
a regular approach to describing particles with different spins in the
framework of a theory of scalar fields on the Poincare group. Such fields can
be considered as generating functions for conventional spin-tensor fields. The
cases of 2, 3, and 4 dimensions are elaborated in detail. Discrete
transformations $C,P,T$ are defined for the scalar fields as automorphisms of
the Poincare group. Doing a classification of the scalar functions, we obtain
relativistic wave equations for particles with definite spin and mass. There
exist two different types of scalar functions (which describe the same mass and
spin), one related to a finite-dimensional nonunitary representation and
another one related to an infinite-dimensional unitary representation of the
Lorentz subgroup. This allows us to derive both usual finite-component wave
equations for spin-tensor fields and positive energy infinite-component wave
equations.
