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

Mathematics – Combinatorics

Scientific paper

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Two figures added and some typos fixed

Scientific paper

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
Bal\'azs Szegedy from 2007.

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