Computing the associated cycles of certain harish-chandra modules

Salah Mehdi (1) , Pavle Pandžić (2) , David Vogan (3) , Roger Zierau (4)

1 IECL - Institut Élie Cartan de Lorraine
2 University of Zagreb
3 Department of Mathematics [MIT]
4 OSU - Oklahoma State University [Stillwater]

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.

Mots clés: Dirac index; nilpotent orbit; associated variety; associated cycle; Springer correspondence; Dirac cohomology

Domaines: Mathématiques [math]

Salah Mehdi, Pavle Pandžić, David Vogan, Roger Zierau. Computing the associated cycles of certain harish-chandra modules. Glasnik Matematicki, 2018, 53 (2), pp.275-330. ⟨10.3336/gm.53.2.05⟩. ⟨hal-03336285⟩