Abstract
We study a class of restricted solid-on-solid (RSOS) models related to the quantum group U q (sl( n)) with q a general primitive root of unity. Physical regimes of the models enjoy intriguing equivalence properties under the interchange of the rank n and the relevant level of the affine Lie algebra A n−1 (1) (level-rank-duality) and also the q- and q −-deformations ( q ±1 duality). By using these we give a classification scheme for ferromagnetic and antiferromagnetic orderings at low temperature. We also propose that the level-rank duality is inherited in rational Toda field theories with imaginary coupling constants. This explains the deficiency structure of the conserved currents in a series of deformed non-unitary conformal field theories.
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