M-systems and Cluster algebras

Abstract

The aim of this paper is two-fold: (1) introduce four systems of equations called M-systems and dual M-systems of types $A_n$ and $B_n$ respectively; (2) make a connection between M-systems (dual M-systems) and cluster algebras and prove that the Hernandez-Leclerc conjecture is true for minimal affinizations of types $A_n$ and $B_n$.

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Cited by in corpus (5)

• A geometric $q$-character formula for snake modules
• On the minimal affinizations of type $F_4$
• Non-Minimality of Certain Irregular Coherent Preminimal Affinizations
• Cluster algebras and snake modules
• On the minimal affinizations over the quantum affine algebras of type $C_n$