量子自旋网络在固定单位单位根处的渐近性
Asymptotics of quantum spin networks at a fixed root of unity
摘要：
经典的自旋网络由带状图（即，每个边周围的顶点具有循环排序的抽象图）和其边的自然数的容许着色。自旋网络的标准评估是一个整数。在以前的文章中，我们证明了一个存在定理的标准评估的任意经典自旋网络时，其边的着色是由一个大的自然数标度的渐近性。在本文中，我们推广的结果的情况下，任意价的量子自旋网络的评价在一个固定的单位根。在经典的情况下，我们的证明使用的理论$G$ -函数的André，连同一些新的结果有关的完整和$q$ -完整序列的Wilf-Zeilberger。
英文摘要：
A classical spin network consists of a ribbon graph (i.e., an abstract graph with a cyclic ordering of the vertices around each edge) and an admissible coloring of its edges by natural numbers. The standard evaluation of a spin network is an integer number. In a previous paper, we proved an existence theorem for the asymptotics of the standard evaluation of an arbitrary classical spin network when the coloring of its edges are scaled by a large natural number. In the present paper, we extend the results to the case of an evaluation of quantum spin networks of arbitrary valency at a fixed root of unity. As in the classical case, our proofs use the theory of $G$-functions of André, together with some new results concerning holonomic and $q$-holonomic sequences of Wilf-Zeilberger.
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