8 research outputs found
Computing the associatied cycles of certain Harish-Chandra modules
Let be a simple real linear Lie group with maximal compact
subgroup and assume that . In \cite{MPVZ} we proved that for any representation
of Gelfand-Kirillov dimension ,
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
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