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.
Additional Metadata
Keywords Edge connection matrix, partition function, vertex model, tensor algebra, orthogonal group, invariants
THEME Logistics (theme 3)
Publisher Academic Press
Journal European Journal of Combinatorics
Project Spinoza prijs Lex Schrijver
Regts, G. (2012). The rank of edge connection matrices and the dimension of algebras of invariant tensors. European Journal of Combinatorics, 33(6), 1167–1173.