Tensor invariants for certain subgroups of the orthogonal group
Combinatorics
2012-09-20 v2 Rings and Algebras
Abstract
Let V be an n-dimensional vector space and let On be the orthogonal group. Motivated by a question of B. Szegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society Volume 20, Number 4, 2007), about the rank of edge connection matrices of partition functions of vertex models, we give a combinatorial parameterization of tensors in V \otimes k invariant under certain subgroups of the orthogonal group. This allows us to give an answer to this question for vertex models with values in an algebraically closed field of characteristic zero.
Keywords
Cite
@article{arxiv.1202.3940,
title = {Tensor invariants for certain subgroups of the orthogonal group},
author = {Jan Draisma and Guus Regts},
journal= {arXiv preprint arXiv:1202.3940},
year = {2012}
}
Comments
14 pages, figure. We fixed a few typo's. To appear in Journal of Algebraic Combinatorics