, Volume 156, Issue 1, pp 127-168

Quantum symmetry and braid group statistics inG-spin models

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In two-dimensional lattice spin systems in which the spins take values in a finite groupG we find a non-Abelian “parafermion” field of the formorder x disorder that carries an action of the Hopf algebra , the double ofG. This field leads to a “quantization” of the Cuntz algebra and allows one to define amplifying homomorphisms on the subalgebra that create the and generalize the endomorphisms in the Doplicher-Haag-Roberts program. The so-obtained category of representations of the observable algebra is shown to be equivalent to the representation category of . The representation of the braid group generated by the statistics operator and the corresponding statistics parameter are calculated in each sector.

Communicated by N. Yu. Reshetikhin