Asymptotic Representations of Quantum Affine Superalgebras

Symmetry Integrability and Geometry-Methods and Applications

article

Huafeng Zhang¹ 

[1] Departement Mathematik and Institut für Theoretische Physik

关键词: quantum groups;    superalgebras;    asymptotic representations;    Baxter operators;   

DOI  :  10.3842/SIGMA.2017.066

来源: National Academy of Science of Ukraine

【 摘 要 】

We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called $q$-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.

【 授权许可】

Unknown