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math.RT2025
An introduction to representation-theoretic canonical bases of cluster algebras
Fan Qin
This is an introduction to cluster algebras and their common triangular bases. These bases are Kazhdan-Lusztig-type and serve as the canonical bases of cluster algebras from the re…
math.RT2025
Analogs of the dual canonical bases for cluster algebras from Lie theory
Fan Qin
We construct common triangular bases for almost all the known (quantum) cluster algebras from Lie theory. These bases provide analogs of the dual canonical bases, long anticipated…