Mathematical Research Letters

Volume 19 (2012)

Number 3

The conjugacy relation on unitary representations

Pages: 525 – 535



Greg Hjorth (Mathematics Department, University of California at Los Angeles)

Asger Törnquist (Department of Mathematics, University of Copenhagen, Denmark)


In a 1965 paper, E.G. Effros asked the question if the conjugacy relation for unitary representations of a locally compact second countable group is a Borel equivalence relation. In this paper, we answer this question affirmatively. This also settles a recent question raised by A.S. Kechris regarding the hierarchy complexity of unitary equivalence of probability measure preserving actions of countable discrete groups.

2010 Mathematics Subject Classification

03E15, 03E75, 22D10, 22D25, 46Lxx

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