Cyclic Haagerup-Izumi fusion categories at every odd order

Tzu-Chen Huang

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arXiv · 2609.15986

Cyclic Haagerup-Izumi fusion categories at every odd order

Tzu-Chen Huang

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Abstract

We construct a complex spherical fusion category with cyclic Haagerup-Izumi fusion rules for every odd n >= 3, and deduce pseudo-unitary existence. The proof has four parts: explicit real coefficients and their quadratic identities; a contour calculation for a range of cubic Fourier coefficients; algebraic completion of all cubics; and categorical reconstruction. Matrix inversion supplies reflection, and an extension of the dimension-field automorphism supplies the positive-dimensional category.

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Tzu-Chen Huang. 2026-09-14. Cyclic Haagerup-Izumi fusion categories at every odd order. https://arxiv.org/abs/2609.15986

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