Toroidal and level 0 U'_q(\hat{sl_{n+1}}) actions on U_q(\hat{gl_{n+1}}) modules

Details Toroidal and level 0 U'_q(\hat{sl_{n+1}}) actions on U_q(\hat{gl_{n+1}}) modules Toroidal and level 0 U'_q(\hat{sl_{n+1}}) actions on U_q(\hat{gl_{n+1}}) modules

1998-08-05

arxiv.org/abs/math/9808023v1

Mathematics

Quantum Algebra

Latex, 20 pages

Scientific paper

(1) Utilizing a Braid group action on a completion of U_q(\hat{sl_{n+1}}), an algebra homomorphism from the toroidal algebra U_q(sl_{n+1,tor}) (n\ge 2) with fixed parameter to a completion of U_q(\hat{gl_{n+1}}) is obtained. (2) The toroidal actions by Saito induces a level 0 U'_q(\hat{sl_{n+1}}) action on level 1 integrable highest weight modules of U_q(\hat{sl_{n+1}}). Another level 0 U'_q(\hat{sl_{n+1}}) action is defined by Jimbo, et al., in the case n=1. Using the fact that the intertwiners of U_q(\hat{sl_{n+1}}) modules are intertwiners of toroidal modules for an appropriate comultiplication, the relation between these two level 0 U'_q(\hat{sl_{n+1}}) actions is clarified.

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