Weyl Quantization from geometric quantization

In [1] a nice looking formula is conjectured for a deformed product of functions on a symplectic manifold in case it concerns a hermitian symmetric space of non-compact type. We derive such a formula for simply connected symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional symplectic manifolds R-2, H-2, and S-2. For R-2 we obtain the well known Moyal-Weyl product. The other cases show that the original idea in [1] should be interpreted with care.