Yangians and quantum loop algebras

By Sachin Gautam, Valerio Toledano Laredo. 2010

83 citations recorded by the source corpus.

Let $$\mathfrak{g }$$ be a complex, semisimple Lie algebra. Drinfeld showed that the quantum loop algebra $$U_\hbar (L\mathfrak g )$$ of $$\mathfrak{g }$$ degenerates to the Yangian $${Y_\hbar (\mathfrak g )}$$. We strengthen this result by constructing an explicit algebra homomorphism $$\Phi $$ from $$U_\hbar (L\mathfrak g )$$ to the completion of $${Y_\hbar (\mathfrak g )}$$ with respect to its grading. We show moreover that $$\Phi $$ becomes an isomorphism when $${U_\hbar (L\mathfrak g )}$$ 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 $$U_\hbar (L\mathfrak gl _{n})$$ 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0c0d7e1234746606852e5ffbb6fff3dfd5185ab4

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In Algebra and Number Theory

  1. V. Toledano-Laredo
  2. Yaping Yang
  3. Gufang Zhao
  4. Sachin Gautam

In Geometry and Topology

  1. V. Toledano-Laredo
  2. Yaping Yang
  3. Gufang Zhao
  4. Sachin Gautam

In Mathematical Physics

  1. V. Toledano-Laredo
  2. Yaping Yang
  3. Sachin Gautam
  4. Gufang Zhao

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