caa a22 4500 606160701 CHVBK 20210128100631.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10468-015-9549-4 doi (NATIONALLICENCE)springer-10.1007/s10468-015-9549-4 Mansuy Mathieu University Paris-Diderot-Paris 7, IMJ - PRG CNRS UMR 7586, Bât. Sophie Germain, Case 7012, 75205, Paris Cedex 13, France aut Extremal Loop Weight Modules for U q ( sl ̂ ∞ ) $\mathcal {U}_{q}(\hat {sl}_{\infty })$ [Elektronische Daten] [Mathieu Mansuy] We construct by fusion product new families of irreducible representations of the quantum affinization U q ( sl ̂ ∞ ) $\mathcal {U}_{q}(\hat {sl}_{\infty })$ . The action is defined via the Drinfeld coproduct and is related to the crystal structure of semi-standard tableaux of type A ∞ . We call these representations extremal loop weight modules. The main motivations are applications to quantum toroidal algebras U q ( s l n + 1 tor ) $\mathcal {U}_{q}(sl_{n+1}^{tor})$ : we prove the conjectural link between U q ( sl ̂ ∞ ) $\mathcal {U}_{q}(\hat {sl}_{\infty })$ and U q ( s l n + 1 tor ) $\mathcal {U}_{q}(sl_{n+1}^{tor})$ stated in Hernandez (J. Algebra 329, 147-162, 2011) for these families of representations. We recover in this way the extremal loop weight modules obtained in Mansuy (arXiv: 1305.3481 ). Springer Science+Business Media Dordrecht, 2015 Quantum groups nationallicence Representation theory nationallicence Quantum affinizations nationallicence Quantum toroidal algebras nationallicence Drinfeld coproduct nationallicence Crystals nationallicence Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1505-1532 1386-923X 18:6<1505 2015 18 10468 https://doi.org/10.1007/s10468-015-9549-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9549-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mansuy Mathieu University Paris-Diderot-Paris 7, IMJ - PRG CNRS UMR 7586, Bât. Sophie Germain, Case 7012, 75205, Paris Cedex 13, France aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/6(2015-12-01), 1505-1532 1386-923X 18:6<1505 2015 18 10468