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We describe a general construction of irreducible unitary representations ofthe group of currents with values in the semidirect product of a locallycompact subgroup $P_0$ and a one-parameter group ${\mathbb R {}}^*_+=\{r:r>0\}$of automorphisms of $P_0$. This construction is determined by a a faithfulunitary representation of $P_0$ (canonical representation) whose images underthe action of the group of automorphisms tend to the identity representation as$r\to 0$. We apply this construction to the groups of currents of the maximalparabolic subgroups of the groups of motions of the $n$-dimensional real andcomplex Lobachevsky spaces. The obtained representations of the groups ofparabolic currents can be uniquely extended to the groups of currents withvalues in the semisimple groups O(n,1) and U(n,1). This gives a new descriptionof the representations of the groups of currents of these groups constructed inthe 70s and realized in the Fock space. The key role in our construction isplayed by the so-called special representation of the parabolic subgroup $P$and the remarkable $\sigma$-finite measure (Lebesgue measure) $\mathcal L$ inthe space of distributions.

Integral models of unitary representations of current groups with values in semidirect products