Data-scientific study of Kronecker coefficients

Abstract: The Kronecker coefficients are the decomposition multiplicities of the tensor product of two irreducible representations of the symmetric group. Unlike the Littlewood--Richardson coefficients, which are the analogues for the general linear group, there is no known combinatorial description of the Kronecker coefficients, and it is an NP-hard problem to decide whether a given Kronecker coefficient is zero or not. In this talk, we take a data-scientific approach to study whether Kronecker coefficients are zero or not. We show that standard machine-learning classifiers may be trained to predict whether a given Kronecker coefficient is zero or not. Motivated by principal component analysis and kernel methods, we also define loadings of partitions and use them to describe a sufficient condition for Kronecker coefficients to be nonzero.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html