All quantum representations from braided, ribbon, and modular fusion categories are semisimple, proven via non-Abelian Hodge theory and Ocneanu rigidity.
Unitarity of the KZ/Hitchin connection on conformal blocks in genus 0 for arbitrary Lie algebras.Journal de Mathématiques Pures et Appliquées, 98(4):367–389, October 2012
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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.