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

Nonunitary representations of the groups of $U(p,q)$-currents for $q\geq p>1$