论文标题
一排彩色$ \ mathfrak {sl} _ {3} $ jones for Pretzel链接
The one-row colored $\mathfrak{sl}_{3}$ Jones polynomials for pretzel links
论文作者
论文摘要
彩色$ \ Mathfrak {sl} _ {3} $ Jones polyenmial $ j _ {（n_ {1}，n_ {2}）}^{\ Mathfrak {\ Mathfrak {sl} _ {3}}}}（3}}}（l; q） $ \ mathfrak {sl} _ {3} $。通常，很难计算$ j _ {（n_ {1}，n_ {2}）}^{\ mathfrak {\ mathfrak {sl} _ {3}}}}}（l; q）$ for方向链接$ l $。但是，我们计算一排$ \ mathfrak {sl} _ {3} $ colored jones polyenmials $ j _ {（n，0）}^{\ mathfrak {\ mathfrak {sl} _ {3}}}}（p（p（α，β，β，γ）; q）$ pred pred preds.通过设置$ n_ {2} = 0 $，使用Kuperberg的线性绞线理论。此外，我们还显示了$ j _ {（n，0）}^{\ Mathfrak {\ Mathfrak {sl} _ {3}}}（p（2α+1，2β+1,2γ）$的尾巴的存在。
The colored $\mathfrak{sl}_{3}$ Jones polynomial $J_{(n_{1}, n_{2})}^{\mathfrak{sl}_{3}}(L;q)$ are given by a link and an $(n_{1}, n_{2})$-irreducible representation of $\mathfrak{sl}_{3}$. In general, it is hard to calculate $J_{(n_{1}, n_{2})}^{\mathfrak{sl}_{3}}(L;q)$ for an oriented link $L$. However, we calculate the one-row $\mathfrak{sl}_{3}$ colored Jones polynomials $J_{(n, 0)}^{\mathfrak{sl}_{3}}(P(α,β,γ);q)$ for three-parameter families of oriented pretzel links $P(α,β,γ)$ by using Kuperberg's linear skein theory by setting $n_{2}=0$. Furthermore, we show the existence of the tails of $J_{(n, 0)}^{\mathfrak{sl}_{3}}(P(2α+1, 2β+1,2γ);q)$ for the alternating pretzel knots $P(2α+1, 2β+1,2γ)$.
