MATRIX CARTAN SUPERDOMAINS, SUPER TOEPLITZ OPERATORS, AND DEFORMATION QUANTIZATION

We present a general theory of non-perturbative quantization of a class of hermitian symmetric supermanifolds. The quantization scheme is based on the notion of a super Toeplitz operator on a suitable Z2-graded Hilbert space of superholomorphic functions. The quantized supermanifold arises as the C ∗ -algebra generated by all such operators. We prove that our quantization framework reproduces the invariant super Poisson structure on the classical supermanifold as Planck’s constant tends to zero.