The structure of the space of affine Kaehler curvature tensors as a   complex module
  We use results of Matzeu and Nikcevic to decompose the space of affine Kaehler curvature tensors as a direct sum of irreducible modules in the complex setting 
M. Brozos-Vazquez, P. Gilkey, S. Nikcevic
math.DG