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arXiv · 1403.5124

Cluster algebra structure on the finite dimensional representations of $U_q(\widehat{A_{3}})$ for $l$=2

Yan-Min Yang·Zhu-Jun Zheng
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Abstract

In this paper, we prove one case of the conjecture given by Hernandez and Leclerc\cite{HL0}. Specifically, we give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of a simply-laced quantum affine algebra $U_q(\widehat{\g})$. In the procedure, we also give a specific description of compatible subsets of type $E_{6}$. As a conclusion, for every exchange relation of cluster algebra there exists a exact sequence of the full subcategory corresponding to it.

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BibTeXRIS

Yan-Min Yang, Zhu-Jun Zheng. 2014-03-20. Cluster algebra structure on the finite dimensional representations of $U_q(\widehat{A_{3}})$ for $l$=2. https://doi.org/10.1088/1674-1056/24/1/010201

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