Kronecker coefficients from algebras of bi-partite ribbon graphs

Abstract

AbstractBi-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 $$\mathcal {K}(n)$$ 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 $$\mathcal {K}(n)$$ 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 $$\mathcal {K}(n)$$ K ( n ) as Hilbert spaces can be used to give combinatorial algorithms for computing the Kronecker coefficients.