Matrix Cartan Superdomains, Super Toeplitz-Operators, and 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 spaces of super-holomorphic 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.