报告主题：Fusion rules for $\mathbb{Z}_{2}$-orbifolds of affine and parafermion vertex operator algebras
报告人：姜翠波 教授 （上海交通大学）
报告时间：2019年6月12日（周三）14：30
报告地点：校本部G508
邀请人：孙建才
报告摘要：This talk is about the orbifold theory of affine and parafermion vertex operator algebras. It is known that the parafermion vertex operator algebra $K(sl_2,k)$ associated to the integrable highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$ is the building block of the general parafermion vertex operator $K(\mathfrak{g},k)$ for any finite dimensional simple Lie algebra $\mathfrak{g}$ and any positive integer $k$.
We first classify the irreducible modules of $\Z_{2}$-orbifold of the simple affine vertex operator algebra of type $A_1^{(1)}$ and determine their fusion rules. Then we study the representations of the $\Z_{2}$-orbifold of the parafermion vertex operator algebra $K(sl_2,k)$, we give the quantum dimensions, and more technically, fusion rules for the $\mathbb{Z}_{2}$-orbifold of the parafermion vertex operator algebra $K(sl_2,k)$ are completely determined. This talk is based on joint work with Wang Qing.
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