  In this paper we describe the new model of the representations of the current
groups with a semisimple Lie group of the rank one. In the earlier papers of
70-80-th (Araki, Gelfand-Graev-Vershik) had posed the problem about irreducible
representations of the current group for $SL(2,R)$, and was used for this the
well-known Fock space-structure
  That construction could be applied to the arbitrary locally compact group,and
is based on a so called special representation of the original group $G$, with
nontrivial 1-cohomology. A new construction uses the special property of one
dimensional extensions (semi-direct product)of the nilpotent groups which
allows immediately to produce the special representation of the group and then
to apply the quasi-Poisson construction from the previous papers by authors in
order to construct the representation of current group. The parabolic subgroup
of the semisimple Lie group of rank one has such semidirect product, and
special representation of it can be extended onto whole semisimple group. As
result we obtain needed new model of the irreducible representation of
semi-simple current groups.
