Asymptotic Representations of Quantum Affine Superalgebras

TL;DR

This paper investigates the asymptotic behavior of representations of quantum affine superalgebras, constructing inductive systems of modules and deriving generalized Baxter's relations, advancing understanding of their structure and limits.

Contribution

It introduces a new asymptotic limit for inductive systems of modules over quantum affine superalgebras, connecting them to modules over the full algebra.

Findings

Constructed inductive systems of Kirillov-Reshetikhin modules.

Realized inductive limits as modules over the $q$-Yangian.

Derived generalized Baxter's relations for the full quantum group.

Abstract

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.