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

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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 subgroup of the real orthogonal group that stabilizes the vertex model. This answers a question of Balázs Szegedy from 2007.

Highlights

► We characterize the rank of edge connection matrices of partition functions. ► It is equal to the dimension of tensors invariant under a subgroup of O(n). ► The proof is based upon a theorem of A. Schrijver characterizing invariant algebras.

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