A cluster ensemble is a pair of positive spaces (i.e. varieties equipped with positive atlases), coming with an action of a symmetry group . The space is closely related to the spectrum of a cluster algebra [12]. The two spaces are related by a morphism . The space is equipped with a closed -form, possibly degenerate, and the space has a Poisson structure. The map is compatible with these structures. The dilogarithm together with its motivic and quantum avatars plays a central role in the cluster ensemble structure. We define a non-commutative -deformation of the -space. When is a root of unity the algebra of functions on the -deformed -space has a large center, which includes the algebra of functions on the original -space. The main example is provided by the pair of moduli spaces assigned in [7] to a topological surface with a finite set of points at the boundary and a split semisimple algebraic group . It is an algebraic-geometric avatar of higher Teichmüller theory on related to . We suggest that there exists a duality between the and spaces. In particular, we conjecture that the tropical points of one of the spaces parametrise a basis in the space of functions on the Langlands dual space. We provide some evidence for the duality conjectures in the finite type case.