  The near horizon geometry of extremal rotating black hole in arbitrary
dimension possesses SO(2,1)xU(n) symmetry in the special case that all n
rotation parameters are equal. We consider a conformal particle associated with
such a maximally symmetric configuration and derive from it a new integrable
Hamiltonian mechanics with U(n) symmetry. A further reduction of the model is
discussed, which is obtained by discarding cyclic variables. A variant of the
Higgs oscillator and the Poschl-Teller system show up in four and five
dimensions, respectively.
