  We generalize the DeWitt-Virasoro (DWV) construction of arXiv:0912.3987
[hep-th] to tensor representations of higher ranks. A rank-$n$ tensor state,
which is by itself coordinate invariant, is expanded in terms of position
eigenstates that transform as tensors of the same rank. The representation of
the momentum operator in these basis states is then obtained by generalizing
DeWitt's argument in Phys.Rev.85:653-661,1952. Such a representation is written
in terms of certain bi-vector of parallel displacement and its covariant
derivatives. With this machinery at hand we find tensor representations of the
DWV generators defined in the previous work. The results differ from those in
spin-zero representation by additional terms involving the spin connection.
However, we show that the DWV algebra found earlier as a scalar expectation
value remains the same, as required by consistency, as all the additional
contributions conspire to cancel in various ways. In particular, vanishing of
the anomaly term requires the same condition of Ricci-flatness for the
background.
