  We suggest a way to study possible conformal symmetries on black hole
horizons. We do this by carrying out a Kaluza-Klein like reduction of the
Einstein-Hilbert action along the ignorable coordinates of stationary and
axisymmetric black holes. Rigid diffeomorphism invariance of the $m$-ignorable
coordinates then becomes a global $SL(m,R)$ gauge symmetry of the reduced
action. Related to each non-vanishing angular velocity there is a particular
$SL(2,R)$ subgroup, which can be extended to the Witt algebra on the black hole
horizons. The classical Einstein-Hilbert action thus has $k$-copies of infinite
dimensional conformal symmetries on a given black hole horizon, with $k$ being
the number of non-vanishing angular velocities of the black hole.
