论文标题
关于保形网的扭曲表示
On Induction for Twisted Representations of Conformal Nets
论文作者
论文摘要
对于给定的有限索引，包含子同类网$ \ MATHCAL {b} \ subset \ Mathcal {a} $和一个$ g <\ m g <\ mathrm {aut}（\ Mathcal {a}，\ Mathcal {B}）$我们为$ g $ twist的表示形式定义了两个感应程序，这些程序概括了$α^{\ pm} $ - DHR内态性的诱导。一个在$ g $ twist的表示形式的类别中定义的，如$α^ - $ - 诱导。另一个也用编织方式定义，但与$ \ Mathcal {B} \ subset \ Mathcal {a} $相关的Q-System上的$ G $ Equivariant结构以及$ G $的操作。我们以与普通$α$诱导的情况相似的方式来得出这些诱发的内态性的一些特性和公式。我们还为我们的设置显示了$ασ$ -Reciprocity公式的版本。
For a given finite index inclusion of conformal nets $\mathcal{B}\subset \mathcal{A}$ and a group $G < \mathrm{Aut}(\mathcal{A}, \mathcal{B})$, we consider the induction and the restriction procedures for $G$-twisted representations. We define two induction procedures for $G$-twisted representations, which generalize the $α^{\pm}$-induction for DHR endomorphisms. One is defined with the opposite braiding on the category of $G$-twisted representations as in $α^-$-induction. The other is also defined with the braiding, but additionally with the $G$-equivariant structure on the Q-system associated with $\mathcal{B}\subset \mathcal{A}$ and the action of $G$. We derive some properties and formulas for these induced endomorphisms in a similar way to the case of ordinary $α$-induction. We also show the version of $ασ$-reciprocity formula for our setting.
