The level-one global Weyl module of a toroidal Lie algebra is isomorphic to an S^{-1}-twist of a known vertex-operator module, giving closed character formulas.
Vertex Representations for Yangians of Kac-Moody algebras
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abstract
Using vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced affine Yangians.
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Level one Weyl modules for toroidal Lie algebras
The level-one global Weyl module of a toroidal Lie algebra is isomorphic to an S^{-1}-twist of a known vertex-operator module, giving closed character formulas.