正交群的某些子群的张量不变量
Tensor invariants for certain subgroups of the orthogonal group
摘要：
设V是一个n维向量空间，On是一个正交群。由一个B的问题激发。Szegedy（B. Szegedy，Edge coloring models and reflection positivity，Journal of the American Mathematical Society Volume 20，Number 4，2007），关于顶点模型的分拆函数的边连接矩阵的秩，我们给出了在正交群的某些子群下\otimes k不变量中张量的组合参数化。这使我们能够回答这个问题的顶点模型的值在一个代数闭域的特征为零。
英文摘要：
Let V be an n-dimensional vector space and let On be the orthogonal group. Motivated by a question of B. Szegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society Volume 20, Number 4, 2007), about the rank of edge connection matrices of partition functions of vertex models, we give a combinatorial parameterization of tensors in V \otimes k invariant under certain subgroups of the orthogonal group. This allows us to give an answer to this question for vertex models with values in an algebraically closed field of characteristic zero.
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