Geodesic
Extended $T$-System of Type $G_2$
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $G_2$ 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.
Keywords: quantum affine algebra of type $G_2$; minimal affinizations; extended $T$-systems; $q$-characters; Frenkel–Mukhin algorithm. 
@article{SIGMA_2013_9_a53,
     author = {Jian-Rong Li and Evgeny Mukhin},
     title = {Extended $T${-System} of {Type} $G_2$},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2013},
     volume = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a53/}
}
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Jian-Rong Li; Evgeny Mukhin. Extended $T$-System of Type $G_2$. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a53/

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