Cluster Ensembles, Quantization and the Dilogarithm II: The Intertwiner

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This paper is the second part of our paper “Cluster ensembles, quantization, and the dilogarithm” [FG2].1 Its main result is a construction, by means of the quantum dilogarithm, of certain intertwiner operators, which play a crucial role in the quantization of the cluster $\mathcal X$ -varieties and construction of the corresponding canonical representation.