  In a dynamically relaxed cluster around a massive black hole a dense stellar
cusp of old stars is expected to form. Previous observations showed a relative
paucity of red giant stars within the central 0.5 pc in the Galactic Center. By
co-adding spectroscopic observations taken over a decade, we identify new
late-type stars, including the first five warm giants (G2-G8III), within the
central 1 arcsec 2 (0.04 {\times} 0.04 pc^2) of the Galaxy. Our findings
increase the number of late-type stars to 21, of which we present deep spectra
for 16. The updated star count, based on individual spectral classification, is
used to reconstruct the surface density profile of giant stars. Our study, for
the first time, finds a cusp in the surface number density of the
spectroscopically identified old (>3 Gyr) giants population (m K<17) within
0.02-0.4 pc described by a single power law with an exponent {\Gamma}= 0.34
{\pm} 0.04.
