Kronecker coefficients from algebras of bi-partite ribbon graphs

Abstract

Bi-partite ribbon graphs arise in organising the large $N$ expansion of correlators in random matrix models and in the enumeration of observables in random tensor models. There is an algebra $\mathcal{K}(n)$, with basis given by bi-partite ribbon graphs with $n$ edges, which is useful in the applications to matrix and tensor models. The algebra $\mathcal{K}(n)$ is closely related to symmetric group algebras and has a matrix-block decomposition related to Clebsch-Gordan multiplicities, also known as Kronecker coefficients, for symmetric group representations. Quantum mechanical models which use $\mathcal{K}(n)$ as Hilbert spaces can be used to give combinatorial algorithms for computing the Kronecker coefficients.

arXiv comment13 pages, 1 figure. References updated, typos fixed. We thank the Editors Konstantinos Anagnostopoulos, Peter Schupp, George Zoupanos, for the invitation to contribute to this special volume on "Non-commutativity and physics". arXiv admin note: text overlap with arXiv:2010.04054

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