Tensor invariants for certain subgroups of the orthogonal group

Details Tensor invariants for certain subgroups of the orthogonal group Tensor invariants for certain subgroups of the orthogonal group

2012-02-17

arxiv.org/abs/1202.3940v1

Mathematics

Combinatorics

14 pages, figure

Scientific paper

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.

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