A duality map for the quantum symplectic double

14 Nov 2018  ·  Allegretti Dylan G. L. ·

We consider a cluster variety called the symplectic double, defined for an oriented disk with finitely many marked points on its boundary. We construct a canonical map from the tropical integral points of this cluster variety into its quantized algebra of rational functions... As a special case, we obtain a solution to Fock and Goncharov's duality conjectures for quantum cluster varieties associated to a disk with marked points. This extends the author's previous work with Kim on quantum cluster varieties associated to punctured surfaces. read more

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Quantum Algebra High Energy Physics - Theory Geometric Topology