论文标题
模块化$ Q $ - 单位模块
Modular $q$-holonomic modules
论文作者
论文摘要
我们介绍了模块化$ q $ - 单位模块的概念，其基本矩阵定义了具有改进的分析属性的共同体，并表明概括的$ q $ - hyphyphymetric方程以及三个关键$ q $ q $ - $ q $ - 单位模块的复杂Chern-simons理论是模块化的。该概念在概念上解释了结和3个manifolds的量子不变性以及精确和扰动的Chern-simons理论的结构特性，此外，还提供了一种有效的方法来解决相应的线性$ q $ - 差异方程。我们论文的另一种标题强调方程而不是模块，是：模块化线性$ q $ -Difference方程。
We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules of complex Chern--Simons theory are modular. This notion explains conceptually recent structural properties of quantum invariants of knots and 3-manifolds, and of exact and perturbative Chern--Simons theory, and in addition provides an effective method to solve the corresponding linear $q$-difference equations. An alternative title of our paper, emphasising the equations rather than the modules, is: Modular linear $q$-difference equations.
