5,280 research outputs found

### On the extended T-system of type $C_3$

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.Comment: arXiv admin note: substantial text overlap with arXiv:1208.482

### Extended $T$-System of Type $G_2$

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

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