|DATE||September 16 (Mon), 2019|
|TITLE||Cluster algebra structures on module categories over quantum affine algebras|
|ABSTRACT||In this talk, I will explain recent results on cluster algebra structures for quantum affine algebras via generalized Schur-Weyl duality.
We study monoidal categorifications of certain monoidal subcategories $C_J$ of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures coincide and arise from the category of finite-dimensional modules over quiver Hecke algebra of type $A_\infty$ via the generalized quantum Schur-Weyl duality. When the quantum affine algebra is of type A or B, the subcategory coincides with the monoidal category $C_\g^0$ introduced by Hernandez-Leclerc. As a consequence, the modules corresponding to cluster monomials are real simple modules over quantum affine algebras. This is joint work with M. Kashiwara, M. Kim and S.-j. Oh (arXiv:1904.01264)