We study a compatibility relationship between Qin’s dominance order on a cluster algebra
and partial
orderings arising from classifications of simple objects in a monoidal categorification
of
. Our
motivating example is Hernandez and Leclerc’s monoidal categorification
using representations of quantum affine algebras. In the framework
of Kang, Kashiwara, Kim and Oh’s monoidal categorification via
representations of quiver Hecke algebras, we focus on the case of the category
-gmod for a
symmetric finite type
quiver Hecke algebra using Kleshchev and Ram’s classification of irreducible
finite-dimensional representations.
Keywords
quiver Hecke algebras, categorification of cluster
algebras, dominance order
