Cluster algebra structure on the finite dimensional representations of for =2
arXiv:1403.5124 · doi:10.1088/1674-1056/24/1/010201
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 . As a conclusion, for every exchange relation of cluster algebra there exists a exact sequence of the full subcategory corresponding to it.
58 pages, 2 figures. Correct some typoes and add a new example. arXiv admin note: text overlap with arXiv:0903.1452 by other authors