engleski

Computing the associated cycles of certain Harish- Chandra modules

Let Gℝ be a simple real linear Lie group with maximal compact subgroup Kℝ and assume that rank(Gℝ)=rank(Kℝ). In [17] we proved that for any representation X of Gelfand-Kirillov dimension 1/2dim(Gℝ/Kℝ), 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.

(𝔤, K)-module, Dirac cohomology, Dirac index, nilpotent orbit, associated variety, associated cycle, Springer correspondence

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