Abstract
We study solutions of the Knizhnik–Zamolodchikov equation for discrete representations ofSU(2)k at rationallevel k+2 = p/q using a regular basis in which the braid matrices are well defined for all spins. We show that at spinJ = (j+1)p−1 for there are always a subset of 2j+1 solutions closed under the action of the braid matrices. For these fields have integer conformal dimension and all the2j+1 solutions are monodromy free. The action of the braid matrices on these can beconsistently accounted for by the existence of a multiplet of chiral fields with extraSU(2) quantumnumbers (m = −j,...,j). In thequantum group SUq(2), with q = e−i π/(k+2), there is an analogous structure and the related representations aretrivial with respect to the standard generators but transform in a spinj representationof SU(2) under the extended centre.
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