(1) Utilizing a braid group action on a completion of an algebra homomorphism from the toroidal algebra to a completion of is obtained. (2) The toroidal actions by Saito induces a level 0 action on level 1 integrable highest weight modules of Another level 0 action was defined by Jimbo et al., in the case Using the fact that the intertwiners of modules are intertwiners of toroidal modules for an appropriate comultiplication, the relation between these two level 0 actions is clarified.
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