Combinatorics of the q-characters of Hernandez-Leclerc modules

Abstract

Let g be a complex simple Lie algebra and Uq(gˆ) be the corresponding untwisted quantum affine algebra. In this paper, we give a path description of the q-characters of Hernandez-Leclerc modules, show that up to spectral parameter shift, the equivalent classes of Hernandez-Leclerc modules in the Grothendieck ring of the category of finite-dimensional Uq(sln+1ˆ)-modules are cluster variables in the cluster algebra introduced by Hernandez and Leclerc, and finally prove that the geometric q-character formula conjecture is true for Hernandez-Leclerc modules.