  Nuclear fission plays an important role in fundamental and applied science,
from astrophysics to nuclear engineering, yet it remains a major challenge to
nuclear theory. Theoretical methods used so far to compute fission observables
rely on symmetry-breaking schemes where basic information on the number of
particles, angular momentum, and parity of the fissioning nucleus is lost. In
this work, we analyze the impact of restoring broken symmetries in the
benchmark case of $^{240}$Pu.
