  We present the first comprehensive chemical study of a representative sample
of 27 luminous red giant branch (RGB) stars belonging to Liller 1, a complex
stellar system in the Galactic bulge. This study is based on medium-resolution
near-infrared spectra acquired with X-shooter at the Very Large Telescope. We
found a subpopulation counting 22 stars with subsolar metallicity
($<$[Fe/H]$>=-0.31\pm0.02$ and 1$\sigma$ dispersion of 0.08 dex) and with
enhanced [$\alpha$/Fe], [Al/Fe], and [K/Fe] that likely formed early and
quickly from gas that was mainly enriched by type II supernovae, and a
metal-rich population counting 5 stars with supersolar metallicity
($<$[Fe/H]$>$=+0.22$\pm$0.03 and 1$\sigma$ dispersion of 0.06 dex) and roughly
solar-scaled [$\alpha$/Fe], [Al/Fe], and [K/Fe] that formed at later epochs
from gas that was also enriched by type Ia supernovae. Moreover, both
subpopulations show enhanced [Na/Fe], as in the bulge field, about solar-scaled
[V/Fe], and depletion of [C/Fe] and $^{12}$C/$^{13}$C with respect to the solar
values. This indicates that mixing and extra-mixing processes during the RGB
evolution also occur at very high metallicities. Notably, no evidence of a Na-O
anticorrelation, which is considered the fingerprint of genuine globular
clusters, has been found. This challenges any formation scenarios that invoke
the accretion of a molecular cloud or an additional stellar system onto a
genuine globular cluster. The results of this study underline the strong
chemical similarity between Liller 1 and Terzan 5 and support the hypothesis
that these complex stellar systems might be fossil fragments of the epoch of
Galactic bulge formation.
