4 problems

Let $\mathcal{C}$ be a generalized Haagerup category for $\mathbb{Z}_{2n}$. Consider the $\mathbb{Z}_2$-graded extensions constructed above, which give four different fusion catego…

Let $A$ be an abelian group with $A_e\cong\mathbb{Z}_{2^n}\times\mathbb{Z}_2$ for $n\geq2$. Mixed-even-part conjecture. The modular data of the Drinfeld center of the…

Let $A$ be an abelian group with $A_e\cong\mathbb{Z}_{2^{n+1}}$. Cyclic-even-part de-equivariantization conjecture. The modular data of the Drinfeld center of the $\mathbb{Z}_2$-de…

Let the third family of potential modular data be defined by involutive metric groups whose fixed-point subgroups have order $4$, with the stated compatibility conditions. Generali…