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Hernandez and Leclerc proved that the Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional modules of any untwisted quantum affine algebrahas a cluster algebra structure. This makes it possible to compute-characters of real prime simple modules associated to cluster variables as a result of a sequence of cluster mutations. In this paper, for minimal affinizations of type  G2 , we describe a cluster algebra algorithm to compute their-characters and prove the geometric-character formula conjectured by Hernandez and Leclerc.

The q-characters of minimal affinizations of type G 2 arising from cluster algebras