  The coupling between the angular momentum of a compact object and an external
tidal field gives rise to the "rotational" tidal Love numbers, which affect the
tidal deformability of a spinning self-gravitating body and enter the
gravitational waveform of a binary inspiral at high post-Newtonian order. We
provide numerical evidence for a surprising "hidden" symmetry among the
rotational tidal Love numbers with opposite parities, which are associated to
perturbations belonging to separate sectors. This symmetry, whose existence had
been suggested on the basis of a Lagrangian description of the tidal
interaction in a binary system, holds independently of the equation of state of
the star.
