QUANTUM SYMMETRIES IN DISCRETE GAUGE-THEORIES

We analyse the fusion, braiding and scattering properties of discrete non-abelian anyons. These occur in (2 + 1)-dimensional theories where a gauge group G is spontaneously broken down to some discrete subgroup H. We identify the quantumnumbers of the electrically and magnetically charged sectors of the remaining discrete gauge theory, and show that on the quantum level the symmetry group HBAR is extended to the (quasi-triangular) Hopf algebra D(HBAR). A conjugacy class paired with a centralizer representation forms an irreducible representation. The fusion rules for arbitrary discrete non-abelian anyons are completely determined by the nontrivial comultiplication (i.e. tensorproduct) of this algebra. It allows for a clear interpretation of Cheshire charge. Also the braid-matrix R, which determines the statistical properties and the two particle Aharonov-Bohm scattering, is fixed and satisfies the Yang-Baxter equation. Most of our considerations are relevant for discrete gauge theories in (3 + 1)-dimensional space time as well.