# On Sch\"utzenberger modules of the cactus group

@inproceedings{Lim2021OnSM, title={On Sch\"utzenberger modules of the cactus group}, author={Jongmin Lim and Oded Yacobi}, year={2021} }

The cactus group acts on the set of standard Young tableau of a given shape by (partial) Schützenberger involutions. It is natural to extend this action to the corresponding Specht module by identifying standard Young tableau with the Kazhdan-Lusztig basis. We term these representations of the cactus group “Schützenberger modules”, denoted S Sch, and in this paper we investigate their decomposition into irreducible components. We prove that when λ is a hook shape, the cactus group action on S… Expand

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