Uniform bounds for maximal flat periods on $S{L}_n(\mathbb{R})$

Abstract

Let $X$ be a compact locally symmetric space associated to $S{L}_n(\mathbb{R})$ and $Y\subset X$ a maximal flat submanifold, not necessarily closed. Using a Euclidean approximation, we give an upper bound in the spectral aspect for Maass forms integrated against a smooth cutoff function on $Y$ .