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Unitary representations of Fuchsian and Kleinian groups

Let $\Gamma$ be a discrete group that is either Fuchsian ($\Gamma \subseteq \text{PSL}(2,\mathbb R)$) or Kleinian ($\Gamma \subseteq \text{PSL}(2,\mathbb{C})$). I have a unitary representationL $$ \...
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