Due to its proximity, the Milky Way nuclear star cluster provides us with a wealth of data not available in other galactic nuclei. In particular, with adaptive optics, we can observe the detailed properties of individual stars, which can offer insight into the origin and evolution of the cluster. We summarize work on the central parsec of the Galactic center based on imaging and spectroscopic observations at the Keck and Gemini telescopes. These observations include stellar positions in two dimension and the velocity in three dimensions. Spectroscopic observations also enable measurements of the physical properties of individual stars, such as the spectral type and in some cases the effective temperature, metallicity, and surface gravity. We present a review of our latest measurements of the density profiles and luminosity functions of the young and old stars in this region. These observations show a complex stellar population with a young (4-6 Myr) compact star cluster in the central 0.5 pc embedded in an older and much more massive nuclear star cluster. Surprisingly, the old late-type giants do not show a cusp profile as long been expected from theoretical work. The solution to the missing cusp problem may offer us insight into the dynamical evolution of the cluster. Finally, we also discuss recent work on the metallicity of stars in this region and how they might be used to trace their origin. The nuclear star cluster shows a large variation in metallicity ([M/Fe]). The majority of the stars have higher than solar metallicity, with about 6% having [M/Fe] $< -0.5$. These observations indicate that the NSC was not built from the globular clusters that we see today. The formation of the nuclear star cluster is more likely from the inward migration of gas originating in the disk of the Milky Way.
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