Br gamma and He I 2.058 mu m images of the Galactic center reveal that most of the Br gamma emission is associated with interstellar gas but that the He I is largely concentrated on individual, luminous stars that therefore must be hot. High-resolution spectra of these stars, emphasizing He I 2.058 mu m through Br gamma 2.166 mu m, are compared with spectra of 98 hot, luminous stars from the literature and new spectra of 43 luminous galactic emission-line stars including late nitrogen sequence Wolf-Rayet, luminous blue variable (LBV), Oe, Of, and ON supergiant stars. Combining our data with other observations from the literature, the He I sources in the central parsec include approximately five Ofpe/WN stars and one late-WC star. The inferred luminosity and detection of Mg II emission lines in the spectrum of IRS 16NE make it a likely LBV candidate. However, we find six stars with line widths < 500 km s(-1) which defy easy classification, even from the extensive library of comparison spectra we have compiled. Considering the ultraviolet constraints of Serabyn & Lacy and Shields & Ferland and the large number of peculiar hot stars, either we see this stellar population at a very distinctive moment in its evolution, or the conditions of formation or the evolution of the stars must be significantly altered by the environment in the central parsec.