量子${\cal C}$ -多项式的代数
Algebra of quantum ${\cal C}$-polynomials
摘要：
用$SL_q(N)$的对称表示着色的纽结多项式满足作为表示参数的函数的差分方程，这看起来像经典${\cal A}$ -多项式的量子化。然而，它们很难推导和研究。更简单的应该是微分膨胀系数的方程，绰号量子${\cal C}$ -多项式。事实证明，对于每个结，实际上可以导出两个有限阶的差分方程的这些系数，那些移位的自旋$n$的表示和$A=q^N$。因此，${\cal C}$ -多项式更丰富，并形成一个完整的环。我们用各种缺陷零结的例子来证明这一点，主要讨论整个扭曲家族。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
