Monoidal categorification and quantum affine algebras

Abstract

We introduce and investigate new invariants on the pair of modules $M$ and $N$ over quantum affine algebras $U_q^{\prime }(\mathfrak{g})$ by analyzing their associated R-matrices. From new invariants, we provide a criterion for a monoidal category of finite-dimensional integrable $U_q^{\prime }(\mathfrak{g})$-modules to become a monoidal categorification of a cluster algebra.

42 pages

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Cited by in corpus (12)

• Q-data and representation theory of untwisted quantum affine algebras
• Isomorphisms among quantum Grothendieck rings and propagation of positivity
• The $(q,t)$-Cartan matrix specialized at $q=1$
• Deformed Cartan matrices and generalized preprojective algebras I: Finite type
• An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras
• $t$-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras
• Affinization of $q$-oscillator representations of $U_q({\mathfrak{gl}}_n)$
• Affinizations, R-matrices and reflection functors
• Categorical crystals for quantum affine algebras
• Equivariant multiplicities via representations of quantum affine algebras
• Reality determining subgraphs and strongly real modules
• Super duality for quantum affine algebras of type $A$