论文标题
一排彩色$ A_2 $网和$ \ Mathfrak {SL} _3 $ tails的扭曲配方
Twist formulas for one-row colored $A_2$ webs and $\mathfrak{sl}_3$ tails of $(2,2m)$-torus links
论文作者
论文摘要
$ \ mathfrak {sl} _3 $彩色琼斯多项式$j_λ^{\ mathfrak {sl} _3} _3}（l）$是通过用两排Young图$λ$为链接组件涂上链接组件来获得的。尽管很难计算$j_λ^{\ mathfrak {sl} _3}（l）$，但我们可以使用Kuperberg的$ a_2 $ skein Relation对其进行计算。在本文中，我们显示了一些扭曲的公式，其中两条线在$ a_2 $ web空间中以一排年轻的颜色和计算$ j _ {（n，0）}^{\ mathfrak {\ mathfrak {sl} _3} _3}（t（2,2,2m））$（2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2M）$ - torus link。这些显式公式将$ \ mathfrak {sl} _3 $ tail $ t（2200万）$。他们还给出了$ \ mathfrak {sl} _3 $ false theta系列带有一排着色的明确描述，因为$ \ mathfrak {sl} _2 $ t $ t of $ t of $ t of $ t（22亿）$被称为false theta系列。
The $\mathfrak{sl}_3$ colored Jones polynomial $J_λ^{\mathfrak{sl}_3}(L)$ is obtained by coloring the link components with two-row Young diagram $λ$. Although it is difficult to compute $J_λ^{\mathfrak{sl}_3}(L)$ in general, we can calculate it by using Kuperberg's $A_2$ skein relation. In this paper, we show some formulas for twisted two strands colored by one-row Young diagram in $A_2$ web space and compute $J_{(n,0)}^{\mathfrak{sl}_3}(T(2,2m))$ for an oriented $(2,2m)$-torus link. These explicit formulas derives the $\mathfrak{sl}_3$ tail of $T(2,2m)$. They also give explicit descriptions of the $\mathfrak{sl}_3$ false theta series with one-row coloring because the $\mathfrak{sl}_2$ tail of $T(2,2m)$ is known as the false theta series.
