All quantum representations from braided, ribbon, and modular fusion categories are semisimple, proven via non-Abelian Hodge theory and Ocneanu rigidity.
Compactifying the space of stable maps.Journal of the American Mathematical Society, 15(1):27–75, January 2002
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Semisimplicity of conformal blocks
All quantum representations from braided, ribbon, and modular fusion categories are semisimple, proven via non-Abelian Hodge theory and Ocneanu rigidity.