Computing the associated cycles of certain harish-chandra modules

International audienceLet 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 2 dim(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