论文标题
量子$ {\ cal C} $ - 多项式的代数
Algebra of quantum ${\cal C}$-polynomials
论文作者
论文摘要
结多项式用$ sl_q（n）$的对称表示为表示差异方程式作为表示参数的函数，看起来像经典$ {\ cal a} $ - 多项式的量化。但是，它们很难得出和调查。应该更简单的是昵称为量子$ {\ cal c} $多项式系数的系数的方程。事实证明，对于每个结，实际上可以得出这些系数有限顺序的两个差异方程，这些系数的旋转$ n $在表示形式的旋转$ n $中，$ a = q^n $。因此，$ {\ cal c} $ - 多项式更丰富，并形成整个环。我们以各种缺陷为零结的例子来证明这一点，主要讨论整个扭曲家庭。
Knot polynomials colored with symmetric representations of $SL_q(N)$ satisfy difference equations as functions of representation parameter, which look like quantization of classical ${\cal A}$-polynomials. However, they are quite difficult to derive and investigate. Much simpler should be the equations for coefficients of differential expansion nicknamed quantum ${\cal C}$-polynomials. It turns out that, for each knot, one can actually derive two difference equations of a finite order for these coefficients, those with shifts in spin $n$ of the representation and in $A=q^N$. Thus, the ${\cal C}$-polynomials are much richer and form an entire ring. We demonstrate this with the examples of various defect zero knots, mostly discussing the entire twist family.
