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The energy representation of a gauge group on a Riemannian manifold has beendiscussed by several authors. Y. Shimada has shown the irreducibility forcompact Riemannian manifold, using white noise analysis. In this paper weextend its technique to noncompact Riemannian manifolds which have differentialoperators satisfying some conditions.

White noise analysis on manifolds and the energy representation of a gauge group