  Stellar population studies provide unique clues to constrain galaxy formation
models. So far, detailed studies based on absorption line strengths have mainly
focused on the optical spectral range although many diagnostic features are
present in other spectral windows. In particular, the near-infrared (NIR) can
provide a wealth of information about stars, such as evolved giants, that have
less evident optical signatures. Due to significant advances in NIR
instrumentation and extension of spectral libraries and stellar population
synthesis (SPS) models to this domain, it is now possible to perform in-depth
studies of spectral features in the NIR to a high level of precision. In the
present work, taking advantage of state-of-the-art SPS models covering the NIR
spectral range, we introduce a new set of NIR indices constructed to be
maximally sensitive to the main stellar population parameters, namely age,
metallicity and initial mass function (IMF). We fully characterize the new
indices against these parameters as well as their sensitivity to individual
elemental abundance variations, velocity dispersion broadening, wavelength
shifts, signal-to-noise ratio and flux calibration. We also present, for the
first time, a method to ensure that the analysis of spectral indices is not
affected by sky contamination, which is a major challenge when dealing with NIR
spectroscopy. Moreover, we discuss two main applications: (i) the ability of
some NIR spectral indices to constrain the shape of the low-mass IMF and (ii)
current issues in the analysis of NIR spectral indices for future developments
of SPS modelling.
