On the Casimir number and formal codegree of Haagerup-Izumi fusion rings
Abstract
For any cyclic group Zn, we first determine the Casimir number and determinant of the Haagerup-Izumi fusion ring HIZn, it turns out that they do not share the same set of prime factors. Then we show that all finite-dimensional irreducible representations of HIZn are defined over certain cyclotomic fields. As a direct result, we obtain the formal codegrees of HIZn, which satisfy the pseudo-unitary inequality.
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