Near horizon black holes in diverse dimensions and integrable models

The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)×U(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 Pöschl-Teller system show up in four and five dimensions, respectively.