Cluster algebra structures on module categories over quantum affine algebras

Masaki Kashiwara, Myungho Kim, Se jin Oh, Euiyong Park

Research output: Contribution to journalArticlepeer-review


We study monoidal categorifications of certain monoidal subcategories (Formula presented.) of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures on their Grothendieck rings (Formula presented.) are closely related to the category of finite-dimensional modules over quiver Hecke algebra of type (Formula presented.) via the generalized quantum Schur–Weyl duality functors. In particular, when the quantum affine algebra is of type (Formula presented.) or (Formula presented.), the subcategory coincides with the monoidal category (Formula presented.) introduced by Hernandez–Leclerc. As a consequence, the modules corresponding to cluster monomials are real simple modules over quantum affine algebras.

Original languageEnglish
Pages (from-to)301-372
Number of pages72
JournalProceedings of the London Mathematical Society
Issue number3
StatePublished - Mar 2022


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