A stability conjecture for the colored Jones polynomial
A stability conjecture for the colored Jones polynomial
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有色琼斯多项式的稳定性猜想
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Thao Vuong
中科院分区：
文献类型：
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作者：
S. Garoufalidis;Thao Vuong
我们对简单李代数的固定射线上用不可约表示着色的结的彩色琼斯多项式的系数给出了一个稳定性猜想，并对所有环面结和所有秩为$2的简单李代数进行了验证。我们的猜想是由[Ga2]中给出的$q$完整多项式序列的度和系数的结构定理和引用{GL2}中给出的交替结的彩色琼斯多项式的稳定性定理所激发的。我们用实例计算来说明我们的结果。
We formulate a stability conjecture for the coefficients of the colored Jones polynomial of a knot, colored by irreducible representations in a fixed ray of a simple Lie algebra, and verify it for all torus knots and all simple Lie algebras of rank $2$. Our conjecture is motivated by a structure theorem for the degree and the coefficients of a $q$-holonomic sequence of polynomials given in [Ga2] and by a stability theorem of the colored Jones polynomial of an alternating knot given in cite{GL2}. We illustrate our results with sample computations.