The rank of edge connection matrices and the dimension of algebras of invariant tensors

Abstract

We characterize the rank of edge connection matrices of partition functions of real vertex models, as the dimension of the homogeneous components of the algebra of $G$-invariant tensors. Here $G$ is the sub- group of the real orthogonal group that stabilizes the vertex model. This answers a question of Balázs Szegedy from 2007.

arXiv commentTwo figures added and some typos fixed