Extended T-System of Type G₂

Abstract

We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type G₂ extending the celebrated T-system relations of type G₂. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type G₂. We use this result to obtain explicit formulas for dimensions of all participating modules.