5,280 research outputs found

    On the extended T-system of type C3C_3

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    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 Uqg^U_q \hat{\mathfrak{g}} of type C3C_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 λ1ω1+λ2ω2+λ3ω3\lambda_1 \omega_1 + \lambda_2 \omega_2 + \lambda_3 \omega_3, where at least one of λ1\lambda_1, λ2\lambda_2, λ3\lambda_3 are zero. Using the systems I-IV, we compute the characters of the restrictions of the minimal affinizations in the systems to Uqg 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 TT-System of Type G2G_2

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    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 G2G_2 extending the celebrated TT-system relations of type G2G_2. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type G2G_2. We use this result to obtain explicit formulas for dimensions of all participating modules