WKB approximation, crystals and combinatorics of Young tableaux

TL;DR

This paper reveals how combinatorial algorithms related to Young tableaux emerge naturally from the WKB approximation of a quantum hypergeometric equation's connection matrix, linking quantum analysis with combinatorics.

Contribution

It demonstrates a novel connection between WKB approximation methods and classical combinatorial algorithms for Young tableaux.

Findings

Robinson-Schensted algorithm derived from WKB approximation

Littlewood-Richardson rule explained via quantum hypergeometric connection matrix

Schützenberger involution linked to WKB analysis

Abstract

In this paper, we show how various combinatorial algorithms of Young tableaux naturally arise from the WKB approximation of the connection matrix of quantum confluent hypergeometric equation, including the Robinson-Schensted algorithm, the Littlewood-Richardson rule and the Sch\"utzenberger involution.