I will present an explicit action of the symplectic cactus group, as defined by Halacheva for the Dynkin diagram of a finite root system, on the crystal of Kashiwara-Nakashima tableaux, in terms of the virtualization map due to Baker. Additionally, I will present a "colourful" algorithm which generalizes recent work of Santos' symplectic reversal, in terms of the symplectic jeu de taquin due to Sheats and Lecouvey. We will see many examples along the way.

This is joint work with Olga Azenhas and Mojdeh Tarighat Feller.