  We consider the problem of computation of the correlation functions for the
z-measures with the deformation (Jack) parameters 2 or 1/2. Such measures on
partitions are originated from the representation theory of the infinite
symmetric group, and in many ways are similar to the ensembles of Random Matrix
Theory of $\beta=4$ or $\beta=1$ symmetry types. For a certain class of such
measures we show that correlation functions can be represented as Pfaffians
including $2\times 2$ matrix valued kernels, and compute these kernels
explicitly. We also give contour integral representations for correlation
kernels of closely connected measures on partitions.
