Equivalence of the Brownian and energy representations

Abstract

We consider two unitary representations of the infinite-dimensional groups of smooth paths with values in a compact Lie group. The first representation is induced by quasi-invariance of the Wiener measure, and the second representation is the energy representation. We define these representations and their basic properties, and then we prove that these representations are unitarily equivalent.

This an article to be published in "Zapiski Seminarov POMI" dedicated to the memory of Mi.I.Gordin

Cited by in corpus (2)

• Reflection Positive Stochastic Processes Indexed by Lie Groups
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