Jian-Rong Li, Evgeny Mukhin, “Extended <nobr>$T$</nobr>-System of Type <nobr>$G_2$</nobr>”, SIGMA, 2013, Volume 9,054, 28 pp.

This article is cited in 6 papers

Extended $T$-System of Type $G_2$

Jian-Rong Li^a, 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

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.

MSC: 17B37; 81R50; 82B23

Received: April 3, 2013; in final form August 16, 2013; Published online August 22, 2013

Language: English

DOI: 10.3842/SIGMA.2013.054