Stability conditions on Kuznetsov components of Gushel–Mukai threefolds and Serre functor

We show that the stability conditions on the Kuznetsov component of a Gushel- Mukai threefold, constructed by Bayer, Lahoz, Macri and Stellari, are preserved by the Serre functor, up to the action of the universal cover of GL(2)(+) (III). As application, we construct stability conditions on the Kuznetsov component of special Gushel-Mukai fourfolds.