论文标题
彩色亚历山大多项式的新对称性
A new symmetry of the colored Alexander polynomial
论文作者
论文摘要
我们提出了彩色亚历山大多项式的新型猜想对称性，即量子$ \ mathfrak {sl} _n $不变的量子的专业化。我们通过研究循环膨胀和彩色霍姆蝇-pt多项式的特征扩展来提供支持对称性的参数。我们研究了这种对称性对循环扩展的群体理论结构施加的约束，并为这些约束提供解决方案。对称性是研究多项式结的强大工具，最后我们建议对称性的几种可能的应用。
We present a new conjectural symmetry of the colored Alexander polynomial, that is the specialization of the quantum $\mathfrak{sl}_N$ invariant widely known as the colored HOMFLY-PT polynomial. We provide arguments in support of the existence of the symmetry by studying the loop expansion and the character expansion of the colored HOMFLY-PT polynomial. We study the constraints this symmetry imposes on the group theoretic structure of the loop expansion and provide solutions to those constraints. The symmetry is a powerful tool for research on polynomial knot invariants and in the end we suggest several possible applications of the symmetry.
