The Littlewood-Richardson rule, and related combinatorics

TL;DR

This paper introduces the Littlewood-Richardson rule and explores modern combinatorial techniques like tableau switching and dual equivalence, relating them to historical approaches in representation theory.

Contribution

It presents a proof of the Littlewood-Richardson rule using advanced combinatorial methods and connects these to earlier classical work.

Findings

Proof based on tableau switching and dual equivalence

Connections between modern and classical techniques

Clarification of combinatorial constructions

Abstract

An introduction is given to the Littlewood-Richardson rule, and various combinatorial constructions related to it. We present a proof based on tableau switching, dual equivalence, and coplactic operations. We conclude with a section relating these fairly modern techniques to earlier work on the Littlewood-Richardson rule.