Computing the associated cycles of certain Harish-Chandra modules

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 2 dim(G_R /K_R), the polynomial on the dual of a compact Cartan subalgebra given by the dimension of th...

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Veröffentlicht in:Glasnik matematički 2018-01, Vol.53 (2), p.275-330
Hauptverfasser: Mehdi, Salah, Pandžić, Pavle, Vogan, David, Zierau, Roger
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Pandžić, Pavle
Vogan, David
Zierau, Roger
description 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 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.
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title Computing the associated cycles of certain Harish-Chandra modules
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