  Global polarization of hyperons induced by the local vorticity of the medium
created in heavy-ion collisions at energies 2.3\,GeV$\le\sqrt{s_{NN}}\le$11.5
GeV is calculated in the parton-hadron-string dynamic (PHSD) model. The
separation of spectator nucleons and the fluidization of the generated particle
distributions are performed. The polarization of all anti-hyperon species is
found significantly larger than that of hyperons. The $\overline{\Xi}$ hyperons
are found to be polarized as strong as $\overline{\Lambda}$s but $\Xi$ hyperons
have weaker polarization compared to $\Lambda$s. The $\Omega$ and
$\overline{\Omega}$ polarizations show the strongest dependence on the
collision energy. Despite the strong polarization of the produced $\Lambda$s
and $\overline{\Lambda}$s induced by the vortical flows in the medium, the
observed polarization signal is significantly depleted because of the feed down
from weak and electromagnetic decays of heavier hyperons. Particularly strong
suppression is found to be due to electromagnetic decays of $\Sigma^0$
hyperons, which multiplicities obtained in the transport are poorly constrained
both from the microscopic input of the $\Sigma^0$ production reactions and from
the experimental data. The final $\Lambda(\overline{\Lambda})$ polarization
signal strongly depends on the $\Sigma^0$ multiplicity generated in the model.
With all these effects we can reproduce the measured global $\Lambda$
polarization in collisions at $\sqrt{s_{NN}}=7.7$ and $11.5$ GeV and the global
$\overline{\Lambda}$ polarization at 11.5 GeV. For energies $< 3$ GeV, the
calculated $\Lambda$ polarization is smaller than the observed one. The
polarization of $\Xi(\overline{\Xi})$ hyperons is calculated. The signal of
$\Xi(\overline{\Xi})$ polarization is argued to be insensitive to feed-down
effects and be a more direct probe of the degree of the vorticity in the
system.
