Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 054, 28 pages      arXiv:1208.4821      http://dx.doi.org/10.3842/SIGMA.2013.054
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa

Extended T-System of Type G2

Jian-Rong Li a and Evgeny Mukhin b
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

Received April 03, 2013, in final form August 16, 2013; Published online August 22, 2013

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 G2 extending the celebrated T-system relations of type G2. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type G2. We use this result to obtain explicit formulas for dimensions of all participating modules.

Key words: quantum affine algebra of type G2; minimal affinizations; extended T-systems; q-characters; Frenkel-Mukhin algorithm.

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