Computation of dilated Kronecker coefficients. (January 2018)

• Record Type: Journal Article
• Authors: Baldoni, V.; Vergne, M.; Walter, M.
• Is Part Of: Journal of symbolic computation. Volume 84(2018)
• Page Start: 113
• Page End: 146
• Publication Date: 2018-01
• Subjects: Representation theory -- Kronecker coefficients -- Stretching function -- Quasi-polynomial -- Hilbert series -- Residue calculus -- Polynomial-time algorithm; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.03.005
• Languages: English
• ISSNs: 0747-7171

Abstract

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.