Abstract
We give an interpretation of the Bargman transform as a correspondence between state spaces that is analogous to commonly considered intertwiners in representation theory of finite groups. We observe that the non-commutative torus is nothing else that the range of the star-exponential for the Heisenberg group within the Kirillov's orbit method context. We deduce from this a realization of the non-commutative torus as acting on a Fock space of entire functions.
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