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arXiv · 1305.2098

On the extended T-system of type $C_3$

Jian-Rong Li
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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.

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Jian-Rong Li. 2013-05-09. On the extended T-system of type $C_3$. https://doi.org/10.1007/s10801-014-0546-1

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