The slack data of the recording tableaux in the quantum Littlewood-Richardson map determine its inverse: some applications

TL;DR

This paper introduces the slack of a recording tableau in the quantum Littlewood-Richardson map, showing it can determine the inverse and applying it to symplectic tableaux.

Contribution

It defines the slack of recording tableaux in the quantum LR map and demonstrates its role in computing the inverse and applications to symplectic tableaux.

Findings

Slack data encodes inverse map information.

Enriched slack captures reverse Schensted insertion routes.

Application to $\rak{k}$-highest symplectic tableaux.

Abstract

We introduce the slack of a recording tableau in the quantum Littlewood-Richardson (LR) map and show that it inherits the needed data from LR-Sundaram tableaux to define the inverse of the quantum LR map. Notably this enriched slack information packs the suitable reverse Schensted column insertion routes to compute the inverse. The slack data is then applied to $\mathfrak{k}$-highest symplectic tableaux.