The quantum symmetry group U q of an extended chiral conformal model is determined by the requirement that symmetry transformations commute with braid group statistics operators and by the relation between fusion rules and tensor product expansions of a certain class of U 4 representations. For thermal minimal “ p-models”, involving no more than p − 1 unitary lowest weight representations of the Virasoro algebra Vir, U 4 is the quantum universal enveloping (QUE) algebra U 4(sl(2)) with deformation parameter q satisfying q + q −1 = 2 cos π/ p ( q p = − 1, p = 4, 5,…). To each 2-dimensional local field labelled by a pair of nonnegative integers v, v ̄ (0 ⩽ v, v ̄ ⩽ p − 2) we make correspond an analytic chiral field φ v , of weight Δ v and q- spin I v ̄ . The correlation functions of φ v , transform under an 1-dimensional unitary representation of the braid group. As a result we reproduce the ADE classification of 2-dimensional p models in terms of their extended chiral counterparts. It turns out that U q -extended chiral p-models always involve non-unitary and indecomposable representations of Vir.