MATRIX CARTAN SUPERDOMAINS, SUPER TOEPLITZ-OPERATORS, AND QUANTIZATION

We present a general theory of non-perturbative quantization of a clas s of hermitian symmetric supermanifolds. The quantization scheme is ba sed on the notion of a super Toeplitz operator on a suitable Z2-graded Hilbert spaces of super-holomorphic functions. The quantized superman ifold arises as the C-algebra generated by all such operators. We pro ve that our quantization framework reproduces the invariant super Pois son structure on the classical supermanifold as Planck's constant tend s to zero. (C) 1995 Academic Press, Inc.