We construct the vertex representations of the quantum toroidal algebras Uq(SIn+ 1,tor) . In the classical case the vertex representations are not irreducible. However in the quantum case they are irreducible.
Cite this article
Yoshihisa Saito, Quantum Toroidal Algebras and Their Vertex Representations. Publ. Res. Inst. Math. Sci. 34 (1998), no. 2, pp. 155–177DOI 10.2977/PRIMS/1195144759