Extremal loop weight modules for U_q(sl_∞)

2013/09/17 by Mathieu Mansuy, Mansuy, Mathieu
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.1309.4298

29 pages

arxiv created 2013/09/17 · openalex publication_date 2013/09/17 · arxiv updated 2013/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct by fusion product new irreducible representations of the quantum affinization U_q(sl_∞). 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(sl_n+1^tor): we prove the conjectural link between U_q(sl_∞) 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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