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arXiv · 1804.00226

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

Runlin Zhang
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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.

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Runlin Zhang. 2018-03-31. Limiting distribution of translates of the orbit of a maximal $\mathbb{Q}$-torus from identity on $SL(N,\mathbb{R})/SL(N,\mathbb{Z})$. https://arxiv.org/abs/1804.00226

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