Computation of Dilated Kronecker Coefficients

TL;DR

This paper introduces a novel algorithm leveraging symplectic geometry and residue calculus to compute Kronecker coefficients, providing both individual values and symbolic formulas across polyhedral chambers, with applications to Hilbert series.

Contribution

The paper presents a new geometric and algebraic approach for computing Kronecker coefficients, including symbolic formulas valid on entire chambers, advancing computational methods in representation theory.

Findings

Effective computation of Kronecker coefficients demonstrated

Algorithm produces symbolic formulas on polyhedral chambers

Successfully computes several Hilbert series

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.