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 |
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Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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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ISSN: | 0017-095X 1846-7989 |
DOI: | 10.3336/gm.53.2.05 |