The hyperelliptic mapping class group of a nonorientable surface of genus $g\geq 4$ has a faithful representation into $GL(g^2-1,\mathbb{R})$

Abstract

We prove that the hyperelliptic mapping class group of a nonorientable surface of genus $g\geq 4$ has a faithful linear representation of dimension $g^2-1$ over $\mathbb{R}$.