  The INSPIRE project has built the largest sample of ultra-compact massive
galaxies (UCMGs) at 0.1<z<0.4 and obtained their star formation histories
(SFHs). Due to their preserved very old stellar populations, relics are the
perfect systems to constrain the earliest epochs of mass assembly in the
Universe and the formation of massive early-type galaxies. The goal of this
work is to investigate whether a correlation exists between the degree of
relicness (DoR), quantifying the fraction of stellar mass formed at z>2, and
the other stellar population parameters.We use the Full-Index-Fitting method to
fit the INSPIRE spectra to single stellar population (SSP) models. This allows
us to measure, for the first time, the low-mass end slope of the IMF, as well
as stellar metallicity [M/H], [Mg/Fe], [Ti/Fe] and [Na/Fe] ratios, and study
correlations between them and the DoR. Similarly to normal-sized galaxies,
UCMGs with larger stellar masses have overall higher metallicities. We found a
correlation between the low-mass end of the IMF slope and the DoR, that,
however, breaks down for systems with a more extended SFH. An even stronger
dependency is found between the IMF and the fraction of mass formed at high-z.
At equal velocity dispersion and metallicity, galaxies with a higher DoR have a
dwarf-richer IMF than that of low-DoR counterparts. This might indicate that
the cosmic epoch and formation mechanisms influence the fragmentation of the
star formation cloud and hence might be the explanation for IMF variations
detected in massive ETGs.
