  There is a remarkable connection between the number of quantum states of
conformal theories and the sequence of dimensions of Lie algebras. In this
paper, we explore this connection by computing the asymptotic expansion of the
elliptic genus and the microscopic entropy of black holes associated with
(supersymmetric) sigma models. The new features of these results are the
appearance of correct prefactors in the state density expansion and in the
coefficient of the logarithmic correction to the entropy.
