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 PS18. Our definition generalizes the group with the same name defined for the symplectic Lie algebra by the author in joint work with O. Azenhas and M. Tarighat-Feller.
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