Probing the central regions of nearby compact elliptical galaxies

K-band spectroscopic observations recorded with NIFS+ALTAIR on Gemini North are used to probe the central arcsecond of the compact elliptical galaxies NGC 4486B, NGC 5846A, and M32. The angular resolution of these data is similar to 0.1 FWHM; this corresponds to a spatial scale of 12 pc in NGC 5846A, which is the most distant galaxy in the sample. Indices that probe the strengths of various atomic and molecular features are measured. The central stellar contents of NGC 4486B and NGC 5846A are similar in the sense that they occupy the same regions of the (Ca I, (CO)-C-12), (Na I, (CO)-C-12), and ((CO)-C-13, (CO)-C-12) diagrams. The NGC 4486B and NGC 5846A observations depart from the sequence defined by solar neighborhood giants in the (Na I, (CO)-C-12) diagram in a sense that is consistent with both galaxies having nonsolar chemical mixtures. For comparison, the M32 data are consistent with a chemical enrichment history like that in the Galactic disk; M32 could not have formed from the stripping of a larger elliptical galaxy. The behavior of the near-infrared line indices as a function of radius is also investigated. The stellar content in the central arcsecond of M32 appears to be well mixed. However, the radial behavior of the indices in NGC 4486B and NGC 5846A show complicated behavior, with the gradients that are present at large radii breaking down or reversing within a few tenths of an arcsec of the nucleus. Based on the age gradients predicted from visible wavelength spectra, coupled with the radial behavior of the < Fe I > and (CO)-C-12(2, 0) indices, it is suggested that the nuclear regions of NGC 4486B and NGC 5846A harbor intermediate-age populations.