  Aims. We aim to investigate the stellar population properties, ages, and
metal content of the globular clusters (GCs) in NGC 3311, the central galaxy of
the Hydra I cluster, to better constrain its evolution history. Methods. We
used integral-field spectroscopic data from the Multi-Unit Spectroscopic
Explorer (MUSE) to identify 680 sources in the central region of NGC 3311 and
extract their 1D spectra. An analysis of these sources in terms of
morphologies, radial velocities, and emission lines allowed us to narrow down
our selection to 49 bona fide GC candidates. We split these candidates into two
groups depending on their projected distance to the galaxy center (R), namely
inner (R<20arcsec) and outer (R>20arcsec) GCs. We stacked the extracted 1D
spectra of the inner and outer GC populations to increase the signal-to-noise
ratios (S/Ns) of the resulting spectra and hence allow full-spectrum fitting.
In addition, we also created a stacked spectrum of all GCs in NGC 3311 and one
of the two most central GC candidates. Using the code pPXF, we performed a
stellar population analysis on the four stacked 1D spectra, obtaining
mass-weighted integrated ages, metallicities, and [$\alpha$/Fe] abundances.
Results. All GCs are old, with ages >13.5 Gyr, and they have super-solar
metallicities. Looking at the color distribution, we find that the inner ones
tend to be redder and more metal rich than the outer ones. This is consistent
with the two-phase formation scenario. Looking at the full-spectral fitting
results, at face value the outer GCs have a larger [$\alpha$/Fe] ratio, which
is in line with what is found for the stars that dominate the surface
brightness profile at the same radii. However, the values for outer and inner
GCs are consistent within the uncertainties.
