论文标题
$ \ mathfrak {sl} _n $对称大彩色$ r $矩阵
The $\mathfrak{sl}_N$ Symmetrically Large Coloured $R$ Matrix
论文作者
论文摘要
对于每个结$ k $和lie代数$ \ mathfrak {g} $，都有一个gukov-manolescu系列，表示$ f^{\ mathfrak {g}} _ k $，它是与量子irredibilsible irrediblesible of redred-nigred-mathake $相关的分析性延续$ n $ n n $ n n $ n n $ n n $ n n $ n n $ n $ nthemiants。在计算$ \ mathfrak {g} = \ mathfrak {sl} _2 $的情况下，已经完成了很多工作，但是工作相对较少的工作研究了其他lie代数。在本文中，我们将大颜色$ r $矩阵从$ \ mathfrak {sl} _2 $扩展到对称颜色的$ \ mathfrak {sl} _n $。这给出了$ f^{\ mathfrak {sl} _n，sym} _k $的定义，用于正编织结，允许预测$ f^{\ mathfrak {sl} _n，sym} _k $，用于更大的结和链接。它还为$ f_k $的猜想的homfly-pt Analouge提供了进一步的证据。
For every knot $K$ and lie algebra $\mathfrak{g}$, there is a Gukov-Manolescu series denoted $F^{\mathfrak{g}}_K$ which serves as an analytic continuation of the quantum knot invariants associated to finite dimensional irreducible representations of $\mathfrak{g}$. There has been a great deal of work done on computing this invariant for $\mathfrak{g} = \mathfrak{sl}_2$ but comparatively less work has studied other lie algebras. In this paper we extend the large colour $R$ matrix from $\mathfrak{sl}_2$ to symmetrically coloured $\mathfrak{sl}_N$. This gives a definition for $F^{\mathfrak{sl}_N, sym}_K$ for positive braid knots and allows for predictions of $F^{\mathfrak{sl}_N, sym}_K$ for a much larger class of knots and links. It also provides further evidence towards a conjectural HOMFLY-PT analouge of $F_K$.
