  It was proposed recently that the near-horizon states of an extremal
four-dimensional Kerr black hole could be identified with a certain chiral
conformal field theory whose Virasoro algebra arises as an asymptotic symmetry
algebra of the near-horizon Kerr geometry. Supportive evidence for the proposed
duality came from the equality of the microscopic entropy of the CFT,
calculated by means of the Cardy formula, and the Bekenstein-Hawking entropy of
the extremal Kerr black hole. In this paper we examine the proposed Kerr/CFT
correspondence in a broader context. In particular, we show that the
microscopic entropy and the Bekenstein-Hawking entropy agree also for the
extremal Kerr-AdS metric in four dimensions, and also for the extremal Kerr-AdS
metrics in dimensions 5, 6 and 7. General formulae for all higher dimensions
are also presented.
