arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2003.12278math.GTmath.QA
收藏

$(2,2m)$ -圆环链的单排着色$A_2$网和$\mathfrak{sl}_3$尾部的扭转公式

Twist formulas for one-row colored $A_2$ webs and $\mathfrak{sl}_3$ tails of $(2,2m)$-torus links

Wataru Yuasa

备注：
19 pages; v2: Theorem 4.7 is corrected, and added some references
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

利用两行杨氏图$λ$对链路元件进行着色，得到$\mathfrak{sl}_3$着色琼斯多项式$J_λ^{\mathfrak{sl}_3}(L)$。虽然一般情况下计算$J_λ^{\mathfrak{sl}_3}(L)$比较困难，但我们可以利用Kuperberg的$A_2$绞链关系来计算它。本文给出了$A_2$网空间中被单行Young图着色的两股绞合链的计算公式，并计算了有向$(2,2m)$ -环面链的$J_{(n,0)}^{\mathfrak{sl}_3}(T(2,2m))$.这些显式公式导出$T(2,2m)$的$\mathfrak{sl}_3$尾部。他们还给出了明确的描述$\mathfrak{sl}_3$假θ系列与单行着色，因为$T(2,2m)$的$\mathfrak{sl}_2$尾部被称为假θ系列。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑