奇数阶循环Haagerup-Izumi融合范畴
Cyclic Haagerup-Izumi fusion categories at every odd order
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中文总结 AI 辅助
针对每个奇数n≥3构造循环Haagerup-Izumi融合范畴，通过四步证明实现伪酉存在性，并利用矩阵求逆与维数域自同构扩展获得反射与正维数结构。
中文摘要 AI 辅助
我们为每个奇数n≥3构造了具有循环Haagerup-Izumi融合规则的复球面融合范畴，并推导出伪酉存在性。证明分为四部分：显式实系数及其二次恒等式；对一系列三次傅里叶系数的围道计算；所有三次项的代数量完备化；以及范畴重构。矩阵求逆提供反射，维数域自同构的扩展提供正维数范畴。
英文摘要
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.
