Multiplicity-free Kronecker products of characters of the symmetric groups

TL;DR

This paper classifies all multiplicity-free tensor products of irreducible and skew characters of symmetric groups, confirming a conjecture and providing formulas for their decomposition.

Contribution

It offers a complete classification of multiplicity-free tensor products of symmetric group characters and skew characters, and derives explicit decomposition formulas.

Findings

Confirmed Bessenrodt's conjecture on multiplicity-free products.

Classified all multiplicity-free tensor products of skew characters.

Derived formulas for decomposing these tensor products.

Abstract

We provide a classification of multiplicity-free inner tensor products of irreducible characters of symmetric groups, thus confirming a conjecture of Bessenrodt. Concurrently, we classify all multiplicity-free inner tensor products of skew characters of the symmetric groups. We also provide formulae for calculating the decomposition of these tensor products.