Geodesic
Tensor invariants for certain subgroups of the orthogonal group
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 393-405.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let V be an n-dimensional vector space, and let O $_{ n }$ be the orthogonal group. Motivated by a question of B. Szegedy (J. Am. Math. Soc. $20(4), 2007)$, 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: edge connection matrix, graph invariant, partition function, orthogonal group, tensor invariants, vertex model 
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     author = {Draisma, Jan and Regts, Guus},
     title = {Tensor invariants for certain subgroups of the orthogonal group},
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     pages = {393--405},
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     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a4/}
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Draisma, Jan; Regts, Guus. Tensor invariants for certain subgroups of the orthogonal group. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 393-405. http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a4/