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Let G be a compact Lie group with Lie algebra V. Consider the Wiener measure P on the space WG = {g: [0, 1]G, g continuous, g(O) = e} For each h in the Cameron-Martin space H over V , let ah be the associated right invariant vector field over WG and let 9; be its adjoint with respect to P . We prove for a particular h that the space of functions on WG generated by CO' -cylindrical functions on WG together with one Gaussian random variable is a core for the Dirichlet operator ah This is the first step in proving the essential selfadjointness of the Number operator over group-valued path spaces in the natural presumed core.

On the essential selfadjointness of Dirichlet operators on group-valued path space