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A limit formula for elliptic orbital integrals. (English) Zbl 1010.22022
The computation of the canonical measure on a nilpotent orbit (through differentiation of the canonical measures on the semisimple orbits) is strictly related to Fourier inversion of the nilpotent orbital integrals. The so-called limit formulas arise in this way. Since the work of Harish-Chandra on the Plancherel formula, the problem of computing the nilpotent measures was intensively studied. The aim of the present paper is to find a limit formula for the class of nilpotent orbits that arise as the leading orbits in the wave-front set of an \(A_q (\lambda)\)-module. The author establishes a limit formula for the computation of the canonical measure on a nilpotent orbit by means of differentiation of the canonical measures on elliptic orbits.

MSC:
22E46 Semisimple Lie groups and their representations
22E30 Analysis on real and complex Lie groups
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