Extremal loop weight modules for $U_q(\hat{sl}_\infty)$
Abstract
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 semistandard 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 [14] for this family of representations. We recover in this way the extremal loop weight modules obtained in [23].
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 arXiv:
 arXiv:1309.4298
 Bibcode:
 2013arXiv1309.4298M
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 29 pages