The goals of this work are to develop a new method to separate early and late type stellar components of a dense stellar cluster based on narrow band filters, to apply it to the central parsec of the GC, and to conduct a population analysis of this area. We use AO assisted observations obtained at the ESO VLT in the NIR H-band and 7 intermediate bands covering the NIR K-band. A comparison of the resulting SEDs with a blackbody of variable extinction then allows us to determine the presence and strength of a CO absorption feature to distinguish between early and late type stars. The new method is suitable to classify K giants (and later) as well as B2 main sequence (and earlier) stars which are brighter than 15.5 mag in the K band in the central parsec. Compared to previous spectroscopic investigations that are limited to 13-14 mag, this represents a major improvement in the depth of the observations as well as reducing the needed observation time. We classify 312 stars as early type candidates out of a sample of 5914 sources. The distribution of the early type stars can be fitted with a steep power law (beta(R>1'') = -1.49 +/- 0.12, alternatively with a broken power law, beta(R=1-10'') = -1.08 +/- 0.12, beta(R=10-20'') = -3.46 +/- 0.58, since we find a drop of the early type density at ~10''). We also detect early type candidates outside of 0.5 pc in significant numbers for the first time. The late type density function shows an inversion in the inner 6'', with a power law slope of beta(R<6'') = 0.17 +/- 0.09. The late type KLF has a power law slope of 0.30$\pm$0.01, closely resembling the KLF obtained for the bulge of the Milky Way. The early type KLF has a much flatter slope of 0.14 +/- 0.02. Our results agree best with an in-situ star formation scenario.