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arXiv · 1309.4298

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

Mathieu Mansuy
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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 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 [14] for this family of representations. We recover in this way the extremal loop weight modules obtained in [23].

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Mathieu Mansuy. 2013-09-17. Extremal loop weight modules for $U_q(\hat{sl}_\infty)$. https://arxiv.org/abs/1309.4298

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