Toroidal and level 0 Uq sln+1 actions on Uq gln+1 modules

(1) Utilizing a braid group action on a completion of U-q(<(sl(n+1))over cap>), an algebra homomorphism from the toroidal algebra U-q(sl(n+1,tor))( n greater than or equal to 2) to a completion of U-q(<(gl(n+1))over cap>) is obtained. (2) The toroidal actions by Saito induces a level 0 U-q'(<(sl(n+1))over cap>) action on level 1 integrable highest weight modules of U-q(<(sl(n+1))over cap>). Another level 0 U-q'(<(sl(n+1))over cap>) action was defined by Jimbo et al., in the case n=1. Using the fact that the intertwiners of U-q(<(sl(n+1))over cap>) modules are intertwiners of toroidal modules for an appropriate comultiplication, the relation between these two level 0 U-q'(<(sl(n+1))over cap>) actions is clarified. (C) 1999 American Institute of Physics. [S0022-2488(99)04806-9].