Computing the associated cycles of certain Harish- Chandra modules

Let G(R) be a simple real linear Lie group with maximal compact subgroup K-R and assume that rank(G(R)) = rank(K-R). In [MPVZ] we proved that for any representation X of Gelfand-Kirillov dimension 1/2dim(G(R)/K-R), the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing X is a linear combination, with integer coefficients, of the multiplicities of the irreducible components occurring in the associated cycle. In this paper we compute these coefficients explicitly.