A limit formula for real Richardson orbits

Abstract

Let $G_\mathbb R$ be a real, semisimple, linear and connected Lie group. Let $K$ denote the complexification of a maximal compact group of $G_\mathbb R$. Assume that $G_\mathbb R$
has a compact Cartan subgroup. We prove a formula which computes the Liouville measure on a real nilpotent Richardson orbit,
obtained by the Sekiguchi correspondence from a $K$-nilpotent Richardson orbit, as a limit of differentiated measures on regular elliptic orbits.