论文标题
Verlinde环与子因子之间的水平对应关系
A Level-Depth Correspondence between Verlinde Rings and Subfactors
论文作者
论文摘要
我们在Verlinde环的水平和子因子的深度之间建立了对应关系。给定简单的紧凑型谎言组$ g $的$ l $ - 级verlinde环$ r_l（g）$，基本表示的张量产品使我们包含一对$ \ text {ii} _1 _1 $ ractor $ n \ subset m $。对于$ n \ subset m $的深度$ d $，我们首先证明$ d = l $ type $ a_n，c_n $和$ b_2 $。更一般而言，显示$ d $的深度$ d $满足$β\ cdot l \ leq d \ leq d \ leq l $，其中$β\ in（0,1）$，其中$β$由简单类型的$ g $独特地确定。我们还表明，$ l^2（m）$中包含的简单$ n $ - $ n $ -bimodules生成了Verlinde Ring $ r_l（g）$作为其融合类别。
We establish a correspondence between the levels of Verlinde rings and the depths of subfactors. Given the $l$-level Verlinde ring $R_l(G)$ of a simple compact Lie group $G$, the tensor products of fundamental representations give us the inclusion of a pair of $\text{II}_1$ factors $N\subset M$. For the depth $d$ of $N\subset M$, we first prove $d=l$ for type $A_n,C_n$ and $B_2$. More generally, the depth $d$ is shown to satisfy $β\cdot l\leq d\leq l$ with $β\in (0,1)$, where $β$ is uniquely determined by the simple type of $G$. We also show that the simple $N$-$N$-bimodules contained in $L^2(M)$ generate the Verlinde ring $R_l(G)$ as its fusion category.
