We characterize the virtual link invariants that can be described as partition function of a real-valued R-matrix, by being weakly reflection positive. Weak reflection positivity is defined in terms of joining virtual link diagrams, which is a specialization of joining virtual link diagram tangles. Basic techniques are the first fundamental theorem of invariant theory, the Hanlon–Wales theorem on the decomposition of Brauer algebras, and the Procesi–Schwarz theorem on inequalities for closed orbits.

中文翻译：

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关于虚链接不变量的实R矩阵的存在性

我们通过弱反射正来表征可以描述为实值 R 矩阵的分区函数的虚拟链接不变量。弱反射正性定义为加入虚链图，这是加入虚链图缠结的特化。基本技术是不变理论的第一个基本定理、关于布劳尔代数分解的 Hanlon-Wales 定理和关于闭合轨道不等式的 Procesi-Schwarz 定理。