The conjugacy relation on unitary representations

TL;DR

This paper proves that the relation of unitary conjugacy among unitary representations of certain groups is a Borel equivalence relation, contributing to the understanding of the descriptive set-theoretic complexity of representation classification.

Contribution

It establishes that the conjugacy relation for unitary representations of second countable locally compact groups is a Borel equivalence relation, a novel result in the field.

Findings

The conjugacy relation is Borel for these groups.

Provides a framework for classifying unitary representations.

Advances descriptive set theory in representation analysis.

Abstract

We show that the unitary conjugacy relation for unitary representations of a second countable locally compact group on a separable Hilbert space is a Borel equivalence relation.