Twisted Fock representations of noncommutative Kähler manifolds

We introduce twisted Fock representations of noncommutative Kahler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by applying creation operators to a vacuum state. “Twisted” means that creation operators are not Hermitian conjugate of annihilation operators in this representation. In deformation quantization of Kahler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the Kahler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative Kahler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative Kahler manifolds concretely.