We report results of a time series analysis of high-resolution K-band imaging, photometry, and polarimetry of stars in the Galactic center cluster covering 7 consecutive years. In our statistical sample with mK<13, about half of the stars show indication of variability consistent with most of them being long-period variable, asymptotic giant branch stars. Some long-period variables already proposed in the literature are confirmed. They are identified with asymptotic giant branch stars. For the first time we show that the bright He I source IRS 16SW is a short-period variable with a period of ~9.72 days. It is most likely an eclipsing binary with a lower mass limit of >=100 solar masses. This confirms previous modeling of characteristics of the near-infrared spectra, which also indicated that IRS 16SW is a massive, young hot star. We also present the results of a polarization survey covering the central parsec of the Galaxy. Stars whose polarization vectors differ from the overall polarization, which is parallel to the Galactic plane, are mostly situated in the ``minispiral'', a region of high thermal flux density at centimeter-radio wavelengths. Some of these sources appear extended in the high-resolution images and have featureless red spectra. We interpret these objects as young stars that may have just recently been formed and are still embedded in a dust shell.
Subject headings: Stars: Binaries:Eclipsing, Galaxy: Center,
Polarization, Stars:Variables:Other (Long-Period Variables)