Limiting distribution of translates of the orbit of a maximal $\mathbb{Q}$-torus from identity on $SL(N,\mathbb{R})/SL(N,\mathbb{Z})$

Abstract

Given a maximal $\mathbb{Q}$-torus in $SL(N,\mathbb{Q})$, its orbit from identity coset in $SL(N,\mathbb{R})/SL(N,\mathbb{Z})$ naturally carries a possibly infinite Haar measure. We classify all possible limit measures of it when translated by a sequence of elements from $SL(N,\mathbb{R})$. This is a natural extension of Shapira and Zheng's work where only $\mathbb{Q}$-split tori are considered.