Asymptotic Representations of Quantum Affine Superalgebras

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.