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We announce an explicit construction of a unitary, strongly rational vertex operator algebra $U$ of central charge $8$ inside $V_{E_6\oplus A_2}$, with a ribbon equivalence $\mathrm{Rep}(U)\simeq Z(\mathcal H_3)$ realizing the Haagerup double. The vertex algebra is generated by six affine currents and three specified w...
For every odd integer $N\geq3$, we construct an untwisted Haagerup--Izumi fusion category $\mathcal H_N$ on the negative spherical branch and a simple, self-contragredient, regular, $C_2$-cofinite vertex operator algebra $E_N$ of central charge $-16N$, together with an equivalence of modular fusion categories: \[ \oper...
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