On unitary representations of the group $C_0^\infty(X, G)$, $G=SU_2$

In this paper a family of irreducible unitary representations of the group $G=C_0^\infty(X,SU_2)$ is constructed, where $X$ is an open set in $R^m$, $m\geqslant5$. The group $G$ consists of all infinitely differentiable mappings $X\to SU_2$ with compact support ($=I$ outside some compact set) and is furnished with pointwise multiplication. The author's construction is a modification of the well-known Araki construction. The representations constructed here act in the class of functional on a space dual to a nuclear space and furnished with a Gaussian measure.
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