Email this article Equivalence of the Brownian and Energy Representations
- Authors: Albeverio S.1, Driver B.K.2, Gordina M.3, Vershik A.M.4
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Affiliations:
- Rheinische Friedrich-Wilhelms-Universit¨at
- University of California
- University of Connecticut
- St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State University, Institute of Problems of Transmission of Information
- Issue: Vol 219, No 5 (2016)
- Pages: 612-630
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238641
- DOI: https://doi.org/10.1007/s10958-016-3134-1
- ID: 238641
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Abstract
We consider two unitary representations of infinite-dimensional groups of smooth paths with values in a compact Lie group. The first representation is induced by the 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. Bibliography: 28 titles.
About the authors
S. Albeverio
Rheinische Friedrich-Wilhelms-Universit¨at
Author for correspondence.
Email: albeverio@iam.uni-bonn.de
Germany, Bonn
B. K. Driver
University of California
Email: albeverio@iam.uni-bonn.de
United States, La Jolla, San Diego
M. Gordina
University of Connecticut
Email: albeverio@iam.uni-bonn.de
United States, Storrs
A. M. Vershik
St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State University, Institute of Problems of Transmission of Information
Email: albeverio@iam.uni-bonn.de
Russian Federation, St.Petersburg
