The rank of edge connection matrices and the dimension of algebras of invariant tensors
European Journal of Combinatorics , Volume 33 - Issue 6 p. 1167- 1173
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.
|Keywords||Edge connection matrix, partition function, vertex model, tensor algebra, orthogonal group, invariants|
|THEME||Logistics (theme 3)|
|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.