  We present new high-resolution near-IR spectroscopy and OH maser observations
to investigate the population of cool luminous stars of the young massive
Galactic cluster RSGC1. Using the 2.293\micron CO-bandhead feature, we make
high-precision radial velocity measurements of 16 of the 17 candidate Red
Supergiants (RSGs) identified by Figer et al. We show that F16 and F17 are
foreground stars, while we confirm that the rest are indeed
physically-associated RSGs. We determine that Star F15, also associated with
the cluster, is a Yellow Hypergiant based on its luminosity and spectroscopic
similarity to $\rho$ Cas. Using the cluster's radial velocity, we have derived
the kinematic distance to the cluster and revisited the stars' temperatures and
luminosities. We find a larger spread of luminosities than in the discovery
paper, consistent with a cluster age 30% older than previously thought
(12$\pm$2Myr), and a total initial mass of $(3\pm1) \times 10^{4}$\msun. The
spatial coincidence of the OH maser with F13, combined with similar radial
velocities, is compelling evidence that the two are related. Combining our
results with recent SiO and H$_2$O maser observations, we find that those stars
with maser emission are the most luminous in the cluster. From this we suggest
that the maser-active phase is associated with the end of the RSG stage, when
the luminosity-mass ratios are at their highest.
