The Virtual Cactus Group and Littelmann Paths

Abstract

We define a virtual cactus group and show that the cactus group action on Littelmann paths is compatible with the virtualization map defined by Pan-Scrimshaw. To show this we use the combinatorics of Dynkin diagram foldings. Our definition generalizes the group with the same name recently defined  for the symplectic Lie algebra in recent joint work with Azenhas and Tarighat-Feller.