  The purpose of this paper is to give a construction of representations of the
group of currents for semisimple groups of rank greater than one. Such groups
have no unitary representations in the Fock space, since the semisimple groups
of this form have no nontrivial cohomology in faithful irreducible
representations. Thus we first construct cohomology of the semisimple groups in
nonunitary representations. The principal method is to reduce all constructions
to Iwasawa subgroups (solvable subgroups of the semisimple groups), with
subsequent extension to the original group. The resulting representation is
realized in the so-called quasi-Poisson Hilbert space associated with natural
measures on infinite-dimensional spaces.
  Key words: Iwasawa subgroup, cohomology, group of currents, nonunitary
representations.
