• Corpus ID: 204904803

Fusion Bialgebras and Fourier Analysis

  title={Fusion Bialgebras and Fourier Analysis},
  author={Zhengwei Liu and Sebastien Palcoux and Jinsong Wu},
  journal={arXiv: Quantum Algebra},
We introduce fusion bialgebras and their duals and systematically study their Fourier analysis. As an application, we discover new efficient analytic obstructions on the unitary categorification of fusion rings. We prove the Hausdorff-Young inequality, uncertainty principles for fusion bialgebras and their duals. We show that the Schur product property, Young's inequality and the sum-set estimate hold for fusion bialgebras, but not always on their duals. If the fusion ring is the Grothendieck… 

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