We present a detailed study of the composition of 20 M giants in the Galactic center with 15 of them confirmed to be in the nuclear star cluster. As a control sample we have also observed 7 M giants in the Milky Way disk with similar stellar parameters. All 27 stars are observed using the NIRSPEC spectrograph on the KECK II telescope in the K-band at a resolving power of R = 23,000. We report the first silicon abundance trends versus [Fe/H] for stars in the Galactic center. While finding a disk/bulge-like trend at subsolar metallicities, we find that [Si/Fe] is enhanced at supersolar metallicities. We speculate on possible enrichment scenarios to explain such a trend. However, the sample size is modest and the result needs to be confirmed by additional measurements of silicon and other α-elements. We also derive a new distribution of [Fe/H] and find the most metal-rich stars at [Fe/H] = +0.5 dex, confirming our earlier conclusions that the Galactic center hosts no stars with extreme chemical compositions.