I am looking for an example of a non-continuous homomorphism $G \to GL_r(\mathbb C_p)$ from a profinite (topologically finitely generated) group $G$, where $\mathbb C_p$ is the completion of an algebraic closure $\overline {\mathbb Q}_p$ of the field of $p$-adic numbers $\mathbb Q_p$.
A non-continuous p-adic representation
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representation-theory
p-adic-number-theory