Abstract
The correlated states of an assembly of N multilevel atoms interacting with resonant radiation fields are determined. On the basis of the duality between the permutation group and the linear group, one can construct the internal states for an assembly of N atoms, with n levels each. The possible states are determined by various allowed Young diagrams, corresponding to various representations of the permutation group SN. The collective transition operators are obtained as the generators of the group SU(n).
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