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JP Journal of Geometry and Topology

Abstract:
Guelfand [4], Godement [3] and Harish-Chandra in the fifties up to Toure and Kangni [6, 7] today, among many others have studied spherical functions relatively to the unitary dual of compact groups.

In this paper, we define

-spherical functions relatively to the coadjoint representation of a complex Lie group and examine the nilpotent case.

Keywords and phrases: coadjoint representation,