We will talk about structure of representation spaces of path groups. These representations are induced by quasi-invariance of the Wiener measure on these groups. It has been studied by Albeverio, Hoegh-Krohn, Vershik et al, but we use methods of classifying von Neumann factors due to Connes and Takesaki which were not available at the time. This is a preliminary report on the joint work with S. Albeverio, B. Driver, A.M. Vershik.