Yangians and quantum loop algebras

Details Yangians and quantum loop algebras Yangians and quantum loop algebras

2010-12-16

arxiv.org/abs/1012.3687v1

Mathematics

Quantum Algebra

52 pages

Scientific paper

Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum loop algebra U_h(Lg) of g degenerates to the Yangian Y_h(g). We strengthen this result by constructing an explicit algebra homomorphism Phi defined over Q[[h]] from U_h(Lg) to the completion of Y_h(g) with respect to its grading. We show moreover that Phi becomes an isomorphism when the quantum loop algebra is completed with respect to its its evaluation ideal. We construct a similar homomorphism for g=gl_n and show that it intertwines the geometric actions of the corresponding quantum loop algebra and Yangian on the equivariant K-theory and homology of the variety of n-step flags in C^d.

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