Maximal dilatation on nonorientable surfaces

On each nonorientable surface of even genus $g\ge 4$, we show that the Liechti-Strenner’s polynomial in~\cite{LiechtiStrenner18} gives a maximal dilatation among pseudo-Anosov diffeomorphisms with an orientable invariant foliation. This is proved by showing that this polynomial is irreducible.