Yangians and quantum loop algebras

Let be a complex, semisimple Lie algebra. Drinfeld showed that the quantum loop algebra of degenerates to the Yangian . We strengthen this result by constructing an explicit algebra homomorphism from to the completion of with respect to its grading. We show moreover that becomes an isomorphism when is completed with respect to its evaluation ideal. We construct a similar homomorphism for and show that it intertwines the actions of and on the equivariant -theory and cohomology of the variety of -step flags in constructed by Ginzburg-Vasserot.