  We calculate the contributions to the one-loop determinant for transverse
traceless gravitons in an $n+3$-dimensional Schwarzschild black hole background
in the large dimension limit, due to the $SO(n+2)$-type tensor and vector
fluctuations, using the quasinormal mode method. Accordingly we find the
quasinormal modes for these fluctuations as a function of a fiducial mass
parameter $\Delta$. We show that the behavior of the one-loop determinant at
large $\Delta$ accords with a heat kernel curvature expansion in one lower
dimension, lending further evidence towards a membrane picture for black holes
in the large dimension limit.
