Local algorithms for coplactic switching of Young tableaux

Abstract

We establish an algorithm for the local computation of the "coswitching operation" on a pair of (skew) semistandard Young tableaux, (X,T), such that that T extends X and T is Littlewood-Richardson. In this context, coswitching refers to conjugation of usual tableau switching with Jeu de Taquin rectification. If X is Littlewood-Richardson in addition to T, this algorithm aligns with the "evacuation shuffling" operation defined by Gillespie and Levinson in relation to real Schubert curves. As a result, the algorithm we define has implications in real algebraic geometry.