  Low-mass stars (M<0.4Msun) are thought to comprise the bulk of the stellar
mass of galaxies but they constitute only of order a percent of the bolometric
luminosity of an old stellar population. Directly estimating the number of
low-mass stars from integrated flux measurements of old stellar systems is
therefore possible but very challenging given the numerous variables that can
affect the light at the percent level. Here we present a new population
synthesis model created specifically for the purpose of measuring the low-mass
initial mass function (IMF) down to ~0.1Msun for metal-rich stellar populations
with ages in the range 3-13.5 Gyr. Our fiducial model is based on the synthesis
of three separate isochrones and a combination of optical and near-IR empirical
stellar libraries in order to produce integrated light spectra over the
wavelength interval 0.35mu<lambda<2.4mu at a resolving power of R~2000. New
synthetic stellar atmospheres and spectra have been computed in order to model
the spectral variations due to changes in individual elemental abundances
including C, N, Na, Mg, Si, Ca, Ti, Fe, and generic alpha elements. We
demonstrate the power of combining blue spectral features with surface
gravity-sensitive near-IR features in order to simultaneously constrain the
low-mass IMF, stellar population age, metallicity, and abundance pattern from
integrated light measurements. Finally, we show that the shape of the low-mass
IMF can also be directly constrained by employing a suite of surface
gravity-sensitive spectral features, each of which is most sensitive to a
particular mass interval.
