  We present high-resolution near-infrared spectra, obtained with the NIRSPEC
spectrograph on the W. M. Keck II Telescope, of a collection of hot, massive
stars within the central 25 arcseconds of the Galactic center. We have
identified a total of twenty-one emission-line stars, seven of which are new
radial velocity detections with five of those being classified as He I
emission-line stars for the first time. These stars fall into two categories
based on their spectral properties: 1) those with narrow 2.112, 2.113 micron He
I doublet absorption lines, and 2) those with broad 2.058 micron He I emission
lines. These data have the highest spectral resolution ever obtained for these
sources and, as a result, both components of the absorption doublet are
separately resolved for the first time. We use these spectral features to
measure radial velocities. The majority of the measured radial velocities have
relative errors of 20 kms, smaller than those previously obtained with
proper-motion or radial velocity measurements for similar stellar samples in
the Galactic center. The radial velocities estimated from the He I absorption
doublet are more robust than those previously estimated from the 2.058 micron
emission line, since they do not suffer from confusion due to emission from the
surrounding ISM. Using this velocity information, we agree that the stars are
orbiting in a somewhat coherent manner but are not as defined into a disk or
disks as previously thought. Finally, multi-epoch radial velocity measurements
for IRS 16NE show a change in its velocity presumably due to an unseen stellar
companion.
