Corpus ID: 119570869

Extremal loop weight modules for $U_q(\hat{sl}_\infty)$

  title={Extremal loop weight modules for \$U_q(\hat\{sl\}_\infty)\$},
  author={Mathieu Mansuy},
  • Mathieu Mansuy
  • Published 2013
  • Mathematics
  • We construct by fusion product new irreducible representations of the quantum affinization $U_q(\hat{sl}_\infty)$. The action is defined via the Drinfeld coproduct and is related to the crystal structure of semi-standard tableaux of type $A_\infty$. We call these representations extremal loop weight modules. The main motivations are applications to quantum toroidal algebras $U_q(sl_{n+1}^{tor})$: we prove the conjectural link between $U_q(\hat{sl}_\infty)$ and $U_q(sl_{n+1}^{tor})$ stated in… CONTINUE READING

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