Geodesic
On the extended T-system of type $C_3$
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 2, pp. 577-617.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 is 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 the $q$-characters of minimal affinizations with weights of the form $\lambda_1 \omega_1 + \lambda_2 \omega_2 + \lambda_3 \omega_3$, where at least one of $\lambda_1, \lambda_2, \lambda_3$ is 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.
Classification : 17B37, 81R50, 82B23
Keywords: extended T-systems, quantum affine algebras, Q-characters, Frenkel-Mukhin algorithm 
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     title = {On the extended {T-system} of type $C_3$},
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Li, Jian-Rong. On the extended T-system of type $C_3$. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 2, pp. 577-617. http://geodesic.mathdoc.fr/item/JAC_2015__41_2_a0/