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arXiv · 1410.0837

Asymptotic Representations of Quantum Affine Superalgebras

Huafeng Zhang
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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.

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BibTeXRIS

Huafeng Zhang. 2014-10-03. Asymptotic Representations of Quantum Affine Superalgebras. https://doi.org/10.3842/sigma.2017.066

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