论文标题
来自$ \ mathfrak {sl}（n | m）$ superalgebras的彩色homfly多项式的新颖对称性
A novel symmetry of colored HOMFLY polynomials coming from $\mathfrak{sl}(N|M)$ superalgebras
论文作者
论文摘要
我们提出了彩色homfly多项式的新颖对称性。它关联了一对由$ n $的特定值以不同表示形式着色的多项式，并概括了彩色亚历山大多项式的先前已知的“拖钩”对称性。正如我们所表明的，对称性具有超级甲虫的起源，我们在定性上讨论了对称性。我们的主要重点是这种属性强加于一般组理论结构的限制，即$ \ mathfrak {sl}（n）$权重系统，是在不变性的扰动扩展中产生的。最后，我们证明了它与特征值猜想的紧密关系。
We present a novel symmetry of the colored HOMFLY polynomial. It relates pairs of polynomials colored by different representations at specific values of $N$ and generalizes the previously known "tug-the-hook" symmetry of the colored Alexander polynomial. As we show, the symmetry has a superalgebra origin, which we discuss qualitatively. Our main focus are the constraints that such a property imposes on the general group-theoretical structure, namely the $\mathfrak{sl}(N)$ weight system, arising in the perturbative expansion of the invariant. Finally, we demonstrate its tight relation to the eigenvalue conjecture.
