  We present a kinematic study of the nuclear stellar disk in M31 at infrared
wavelengths using high spatial resolution integral field spectroscopy. The
spatial resolution achieved, FWHM = 0."12 (0.45 pc at the distance of M31), has
only previously been equaled in spectroscopic studies by space-based long-slit
observations. Using adaptive optics-corrected integral field spectroscopy from
the OSIRIS instrument at the W. M. Keck Observatory, we map the line-of-sight
kinematics over the entire old stellar eccentric disk orbiting the supermassive
black hole (SMBH) at a distance of r<4 pc. The peak velocity dispersion is
381+/-55 km/s , offset by 0.13 +/- 0.03 from the SMBH, consistent with previous
high-resolution long-slit observations. There is a lack of near-infrared (NIR)
emission at the position of the SMBH and young nuclear cluster, suggesting a
spatial separation between the young and old stellar populations within the
nucleus. We compare the observed kinematics with dynamical models from Peiris &
Tremaine (2003). The best-fit disk orientation to the NIR flux is [$\theta_l$,
$\theta_i$, $\theta_a$] = [-33 +/- 4$^{\circ}$, 44 +/- 2$^{\circ}$, -15 +/-
15$^{\circ}$], which is tilted with respect to both the larger-scale galactic
disk and the best-fit orientation derived from optical observations. The
precession rate of the old disk is $\Omega_P$ = 0.0 +/- 3.9 km/s/pc, lower than
the majority of previous observations. This slow precession rate suggests that
stellar winds from the disk will collide and shock, driving rapid gas inflows
and fueling an episodic central starburst as suggested in Chang et al. (2007).
