Computing the associatied cycles of certain Harish-Chandra modules

2017/12/12 by Salah Mehdi, Mehdi, Salah, Pavle Pandžić +5 · 1 citation
Mathematics · #22E47 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1712.04173

openalex publication_date 2017/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G_ℝ be a simple real linear Lie group with maximal compact subgroup K_ℝ and assume that \rm rank(G_ℝ)=\rm rank(K_ℝ). In \citeMPVZ 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.

Citations

• Dirac Index and Twisted Characters

Cited by

• Dirac operators for algebraic families

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