Extended $T$-System of Type $G_2$

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 $G_2$ extending the celebrated $T$-system relations of type $G_2$. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type $G_2$. We use this result to obtain explicit formulas for dimensions of all participating modules.

References in corpus (4)

• On minimal affinizations of representations of quantum groups
• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r
• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2
• Path description of type B q-characters

Cited by in corpus (5)

• M-systems and Cluster algebras
• Graded limits of minimal affinizations over the quantum loop algebra of type $G_2$
• On the extended T-system of type $C_3$
• On the minimal affinizations of type $F_4$
• Representations of quantum affine algebras of type $B_N$