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