论文标题
类型$ a $，$ b $，$ c $和$ g $的模块化张量类别的自动等值
Auto-equivalences of the modular tensor categories of type $A$, $B$, $C$ and $G$
论文作者
论文摘要
我们计算模块化张量类别的单型和编织的自动等效率$ \ Mathcal {C}（\ Mathfrak {\ Mathfrak {sl} _ {r+1}，k）$，$ \ Mathcal {c}（c}（c}） $ \ mathcal {c}（\ Mathfrak {sp} _ {2r}，k）$和$ \ Mathcal {C}（\ Mathfrak {g} _ {2}，k）$。除了预期的简单当前自动等效率外，我们还显示了$ \ m athcal {c} {c}（\ Mathfrak {sl} _ {r+1}，k）$和$ \ mathcal {c} $ n offorto自动等值的$ \ mathcal {c}（\ Mathfrak {sl} _ {r+1} _ {r+1}（c} c}（c c} 2））{ $\mathcal{C}(\mathfrak{sp}_{2r},r)$, $\mathcal{C}(\mathfrak{g}_{2},4)$.我们以讨论这些计算的潜在应用的部分结束了论文。
We compute the monoidal and braided auto-equivalences of the modular tensor categories $\mathcal{C}(\mathfrak{sl}_{r+1},k)$, $\mathcal{C}(\mathfrak{so}_{2r+1},k)$, $\mathcal{C}(\mathfrak{sp}_{2r},k)$, and $\mathcal{C}(\mathfrak{g}_{2},k)$. Along with the expected simple current auto-equivalences, we show the existence of the charge conjugation auto-equivalence of $\mathcal{C}(\mathfrak{sl}_{r+1},k)$, and exceptional auto-equivalences of $\mathcal{C}(\mathfrak{so}_{2r+1},2)$, $\mathcal{C}(\mathfrak{sp}_{2r},r)$, $\mathcal{C}(\mathfrak{g}_{2},4)$. We end the paper with a section discussing potential applications of these computations.
