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- W3100532919 abstract "Let $$mathfrak{g }$$ be a complex, semisimple Lie algebra. Drinfeld showed that the quantum loop algebra $$U_hbar (Lmathfrak g )$$ of $$mathfrak{g }$$ degenerates to the Yangian $${Y_hbar (mathfrak g )}$$ . We strengthen this result by constructing an explicit algebra homomorphism $$Phi $$ from $$U_hbar (Lmathfrak g )$$ to the completion of $${Y_hbar (mathfrak g )}$$ with respect to its grading. We show moreover that $$Phi $$ becomes an isomorphism when $${U_hbar (Lmathfrak g )}$$ is completed with respect to its evaluation ideal. We construct a similar homomorphism for $$mathfrak{g }=mathfrak{gl }_n$$ and show that it intertwines the actions of $$U_hbar (Lmathfrak gl _{n})$$ and $$Y_hbar (mathfrak gl _{n})$$ on the equivariant $$K$$ -theory and cohomology of the variety of $$n$$ -step flags in $${mathbb{C }}^d$$ constructed by Ginzburg–Vasserot." @default.
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- W3100532919 date "2012-12-08" @default.
- W3100532919 modified "2023-10-16" @default.
- W3100532919 title "Yangians and quantum loop algebras" @default.
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- W3100532919 doi "https://doi.org/10.1007/s00029-012-0114-2" @default.
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