Local distribution of rational points in flag varieties

Abstract

Given a flag variety $X$ defined over $\mathbb{Q}$ and a point $x$ in $X(\mathbb{R})$, we study approximations to $x$ by points $v$ in $X(\mathbb{Q})$, and show that, with an appropriate rescaling, those approximations equidistribute when $x$ is chosen randomly according to a Lebesgue measure on $X(\mathbb{R})$, or when $x$ is defined over $\mathbb{Q}$ and satisfies some non-degeneracy condition.