Kronecker coefficients from algebras of bi-partite ribbon graphs

Bi-partite ribbon graphs arise in organizing the large N expansion of correlators in random matrix models and in the enumeration of observables in random tensor models. There is an algebra 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 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 𝒦(n) as Hilbert spaces can be used to give combinatorial algorithms for computing the Kronecker coefficients.