Quantization of canonical bases and the quantum symplectic double

Abstract

We describe a natural $q$-deformation of Fock and Goncharov's canonical basis for the algebra of regular functions on a cluster variety associated to a quiver of type $A$. We then describe an extension of this construction involving a cluster variety called the symplectic double.

39 pages. Version 2: Minor corrections and reorganization. Version 3: Changed title and rewrote introduction

References in corpus (5)

• The quantum dilogarithm and representations quantum cluster varieties
• A duality map for quantum cluster varieties from surfaces
• Quantum Teichmüller spaces and quantum trace map
• Categorified canonical bases and framed BPS states
• The cluster symplectic double and moduli spaces of local systems

Cited by in corpus (2)

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