Count lifts of non-maximal closed horocycles on $S{L}_N(\mathbb{Z})\backslash S{L}_N(\mathbb{R})/S{O}_N(\mathbb{R})$

Runlin Zhang

A closed horocycle $\mathcal{U}$ on $S{L}_N(\mathbb{Z})\backslash S{L}_N(\mathbb{R})/S{O}_N(\mathbb{R})$ has many lifts to the universal cover $S{L}_N(\mathbb{R})/S{O}_N(\mathbb{R})$. U…