Differences in representation structure between the Ising minimal model and SU(2)_2 Chern-Simons theory do not impact observables relevant to topological quantum computation.
Geometric quantization of chern-simons gauge theory.Journal of Differential Geometry, 33(3):787–902, 1991
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Ising anyons in the $SU(2)_2$ Chern--Simons theory
Differences in representation structure between the Ising minimal model and SU(2)_2 Chern-Simons theory do not impact observables relevant to topological quantum computation.