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

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 weight symplectic tableaux.