Computation of Dilated Kronecker Coefficients

Abstract

The computation of Kronecker coefficients is a challenging problem with a variety of applications. In this paper we present an approach based on methods from symplectic geometry and residue calculus. We outline a general algorithm for the problem and then illustrate its effectiveness in several interesting examples. Significantly, our algorithm does not only compute individual Kronecker coefficients, but also symbolic formulas that are valid on an entire polyhedral chamber. As a byproduct, we are able to compute several Hilbert series.

This article draws heavily from arXiv:1506.02472. It is an updated version of arXiv:1601.04325. We have clarified the structure and layout of the paper and we have isolated the algorithm into Appendix A, giving a concise exposition of it in pseudo-code and a detailed explanation of all steps, cross-referenced with the main text

References in corpus (4)

• Quantum marginal problem and representations of the symmetric group
• Nested sets and Jeffrey Kirwan cycles
• Multiplicity of compact group representations and applications to Kronecker coefficients
• Computation of the highest coefficients of weighted Ehrhart quasi-polynomials of rational polyhedra

Cited by in corpus (6)

• Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes
• On vanishing of Kronecker coefficients
• Vector partition functions and Kronecker coefficients
• The 144 symmetries of the Littlewood-Richardson coefficients of $S{L}_3$
• Refuting spectral compatibility of quantum marginals
• Weight multiplicity formulas for bivariate representations of classical Lie algebras