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Symmetry, Integrability and Geometry: Methods and Applications, 2013, Volume 9, 054, 28 pp.
DOI: https://doi.org/10.3842/SIGMA.2013.054 (Mi sigma837) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Extended $T$-System of Type $G_2$

Jian-Rong Lia, Evgeny Mukhinb

a Department of Mathematics, Lanzhou University, Lanzhou 730000, P.R. China
b Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 North Blackford St., Indianapolis, IN 46202-3216, USA
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DOI: https://doi.org/10.3842/SIGMA.2013.054
Abstract: 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.
Received: April 3, 2013; in final form August 16, 2013; Published online August 22, 2013
Bibliographic databases:
Document Type: Article
MSC: 17B37; 81R50; 82B23
Language: English
Citation: Jian-Rong Li, Evgeny Mukhin, “Extended $T$-System of Type $G_2$”, SIGMA, 9 (2013), 054, 28 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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