On (almost) extreme components in Kronecker products of characters of the symmetric groups

TL;DR

This paper uses a recursion formula to analyze the structure of Kronecker products of symmetric group characters, confirming a conjecture about products with only three or four components.

Contribution

It applies Dvir's recursion to classify Kronecker products with minimal components, resolving a conjecture from 1999.

Findings

Confirmed the classification of Kronecker products with three or four components.

Identified maximal and almost maximal components in these products.

Provided new insights into the structure of symmetric group characters.

Abstract

Using a recursion formula due to Dvir, we obtain information on maximal and almost maximal components in Kronecker products of characters of the symmetric groups. This is applied to confirm a conjecture made by Bessenrodt and Kleshchev in 1999, which classifies all such Kronecker products with only three or four components.