Is there an example of $G$, $\rho$ as below?

  • $G$ is a locally compact group.

  • $\rho$ is a continuous representation of $G$ on a Hilbert space $V$. This means that we have a homomorphism from $G$ to the group of bounded linear operators on $V$ with bounded inverse, such that $G \times V \rightarrow V$ is continuous.

  • Schur's lemma fails for $\rho$.


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