  A monolayer of WTe$_2$ has been shown to display quantum spin Hall (QSH) edge
modes persisting up to 100~K in transport experiments. Based on
density-functional theory calculations and symmetry-based model building
including the role of correlations and substrate support, we develop an
effective electronic model for WTe$_2$ which fundamentally differs from other
prototypical QSH settings: we find that the extraordinary robustness of quantum
spin Hall edge modes in WTe$_2$ roots in a glide symmetry due to which the
topological gap opens away from high-symmetry points in momentum space. While
the indirect bulk gap is much smaller, the glide symmetry implies a large
direct gap of up to 1~eV in the Brillouin zone region of the dispersing edge
modes, and hence enables sharply boundary-localized QSH edge states depending
on the specific boundary orientation.
