  We prove a criterion for the irreducibility of an integral group
representation \rho over the fraction field of a noetherian domain R in terms
of suitably defined reductions of \rho at prime ideals of R. As applications,
we give irreducibility results for universal deformations of residual
representations, with a special attention to universal deformations of residual
Galois representations associated with modular forms of weight at least 2.
