A limit formula for elliptic orbital integrals

Abstract

Let $\mathcal{O}$ be a nilpotent orbit for a semisimple Lie group which appears as the leading orbit in the wave-front set of an $A_{\mathfrak{q}}(\lambda )$ -module. We establish a limit formula for the computation of the canonical measure on $\mathcal{O}$ through differentiation of the canonical measures on elliptic orbits.