### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 066, 25 pages      arXiv:1410.0837      https://doi.org/10.3842/SIGMA.2017.066

### Asymptotic Representations of Quantum Affine Superalgebras

Huafeng Zhang
Departement Mathematik and Institut für Theoretische Physik, ETH Zürich, Switzerland

Received April 21, 2017, in final form August 17, 2017; Published online August 22, 2017

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.

Key words: quantum groups; superalgebras; asymptotic representations; Baxter operators.

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