On the extended T-system of type $C_3$

Abstract

We continue the study of extended T-systems of quantum affine algebras. We find a sub-system of the extended T-system of the quantum affine algebra $U_q\hat{\mathfrak{g}}$ of type $C_3$. The sub-system consisting of four systems which are denoted by I, II, III, and IV. Each of the systems I, II, III, IV is closed. The systems I-IV can be used to compute minimal affinizations with weights of the form ${\lambda }_1{\omega }_1+{\lambda }_2{\omega }_2+{\lambda }_3{\omega }_3$, where at least one of ${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$ are zero. Using the systems I-IV, we compute the characters of the restrictions of the minimal affinizations in the systems to $U_q\mathfrak{g}$ and obtain some conjectural decomposition formulas for the restrictions of some minimal affinizations.

arXiv admin note: substantial text overlap with arXiv:1208.4821

References in corpus (4)

• On minimal affinizations of representations of quantum groups
• Minimal affinizations as projective objects
• Affinization of category O for quantum groups
• Jacobi-Trudi determinants and characters of minimal affinizations

Cited by in corpus (3)

• M-systems and Cluster algebras
• On the minimal affinizations of type $F_4$
• On the minimal affinizations over the quantum affine algebras of type $C_n$