On the minimal affinizations over the quantum affine algebras of type Cn
Abstract
In this paper, we study the minimal affinizations over the quantum affine algebras of type Cn by using the theory of cluster algebras. We show that the q-characters of a large family of minimal affinizations of type Cn satisfy some systems of equations. These equations correspond to mutation equations of some cluster algebras. Furthermore, we show that the minimal affinizations in these equations correspond to cluster variables in these cluster algebras.
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