Cluster algebra structure on the finite dimensional representations of $U_q(\widehat{A_{3}})$ for $l$=2
Quantum Algebra
2015-06-19 v2 Mathematical Physics
math.MP
Representation Theory
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 . 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.
Keywords
Cite
@article{arxiv.1403.5124,
title = {Cluster algebra structure on the finite dimensional representations of $U_q(\widehat{A_{3}})$ for $l$=2},
author = {Yan-Min Yang and Zhu-Jun Zheng},
journal= {arXiv preprint arXiv:1403.5124},
year = {2015}
}
Comments
58 pages, 2 figures. Correct some typoes and add a new example. arXiv admin note: text overlap with arXiv:0903.1452 by other authors