Symplectic right keys -- Type C Willis' direct way

TL;DR

This paper introduces a direct method for computing symplectic right keys in Kashiwara-Nakashima tableaux, avoiding the traditional jeu de taquin process, inspired by Willis' approach for type A.

Contribution

It presents a novel, jeu de taquin-free technique for calculating symplectic right keys, extending Willis' method from type A to type C.

Findings

Provides a new direct computation method for symplectic right keys.

Eliminates the need for jeu de taquin in symplectic tableau analysis.

Enhances computational efficiency for symplectic key calculations.

Abstract

It is known that the right key of a Kashiwara-Nakashima tableau can be computed using the Lecouvey-Sheats symplectic jeu de taquin. Motivated by Willis' direct way of computing type A right keys, we also give a way of computing symplectic right keys without the use of jeu de taquin.