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 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].
- Publication:
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arXiv e-prints
- Pub Date:
- September 2013
- DOI:
- 10.48550/arXiv.1309.4298
- arXiv:
- arXiv:1309.4298
- Bibcode:
- 2013arXiv1309.4298M
- Keywords:
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- Mathematics - Quantum Algebra
- E-Print:
- 29 pages