Relation of quiver Hecke algebra bases to cluster theory in non-symmetric types

Ascertain the relationship between the bases arising from simple modules of quiver Hecke algebras for non-symmetric Kac–Moody types and cluster algebra structures, including whether and how these bases correspond to or categorify canonical bases such as the common triangular basis in associated cluster algebras.

Background

The paper contrasts representation-theoretic canonical bases (e.g., dual canonical and common triangular bases) with geometric theta bases. It notes that in non-symmetric Kac–Moody types, bases coming from quiver Hecke algebras may be more appropriate, but their connections to cluster theory are currently unclear.

Clarifying this relation would unify perspectives from categorification and cluster algebra theory in non-symmetric settings, potentially identifying new canonical bases compatible with cluster structures.