Geodesic
Nonunitary representations of the groups of $U(p,q)$-currents for $q\geq p>1$
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Tome 462 (2017), pp. 5-38

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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. 
@article{ZNSL_2017_462_a0,
     author = {A. M. Vershik and M. I. Graev},
     title = {Nonunitary representations of the groups of $U(p,q)$-currents for $q\geq p>1$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--38},
     publisher = {mathdoc},
     volume = {462},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a0/}
}
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A. M. Vershik; M. I. Graev. Nonunitary representations of the groups of $U(p,q)$-currents for $q\geq p>1$. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Tome 462 (2017), pp. 5-38. http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a0/