论文标题
在$ \ frak {sl}（2）_ { - 3/2} $和$ \ frak {sl}（3）_ { - 3/2} $的parafermion顶点代数上
On parafermion vertex algebras of $\frak{sl}(2)_{-3/2}$ and $\frak{sl}(3)_{-3/2}$
论文作者
论文摘要
我们研究parafermion顶点代数$ n _ { - 3/2}（\ frak {sl}（2））$和$ n _ { - 3/2}（\ frak {sl}（3））$。使用$ n _ { - 3/2}（\ frak {sl}（3））$与对数顶点algebra $ \ Mathcal {w}^{0}（2）_ {a_2} $ [2]，我们显示这些parafermion verex ered for irire for Irirembras for Irirembras for Irirembras， Zamolodchikov algebra $ \ Mathcal {w}（2,3）$的中央费用$ C = -10 $，以及该$ n _ { - 3/2}（\ frak {sl}（3））$是不可$ n _ { - 3/3/2}（3/3/2}（\ frak frak}）的直接总和。作为副产品，我们证明了有关顶点代数$ \ mathcal {w}^0（p）_ {a_2} $的某些猜想。我们还获得了$ \ Mathcal w（2,3）_ {C} $模块的$ C = -10 $的$ \ Mathcal W（2,3）_ Mathcal W（2,3）的不可约性证明。
We study parafermion vertex algebras $N_{-3/2}(\frak{sl}(2))$ and $N_{-3/2}(\frak{sl}(3))$. Using the isomorphism between $N_{-3/2}(\frak{sl}(3))$ and the logarithmic vertex algebra $\mathcal{W}^{0} (2)_{A_2} $ from [2], we show that these parafermion vertex algebras are infinite direct sums of irreducible modules for the Zamolodchikov algebra $\mathcal{W}(2,3)$ of central charge $c=-10$, and that $N_{-3/2}(\frak{sl}(3))$ is a direct sum of irreducible $N_{-3/2}(\frak{sl}(2))$-modules. As a byproduct, we prove certain conjectures about the vertex algebra $\mathcal{W}^0(p)_{A_2}$. We also obtain a vertex-algebraic proof of the irreducibility of a family of $\mathcal W(2,3)_{c}$ modules at $c=-10$.
