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• W3105365883 abstract "A bstract We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d : it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams." @default.
• W3105365883 created "2020-11-23" @default.
• W3105365883 creator A5000762009 @default.
• W3105365883 creator A5042478789 @default.
• W3105365883 date "2017-11-01" @default.
• W3105365883 modified "2023-10-14" @default.
• W3105365883 title "Tensor models, Kronecker coefficients and permutation centralizer algebras" @default.
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• W3105365883 doi "https://doi.org/10.1007/jhep11(2017)092" @default.
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