J. Korean Math. Soc. 2014; 51(2): 427-442
Printed March 1, 2014
https://doi.org/10.4134/JKMS.2014.51.2.427
Copyright © The Korean Mathematical Society.
Min Kyu Kim and Hyeonmi Lee
Gyeongin National University of Education, Hanyang University
A previous work gave a combinatorial description of the crystal $B(\infty)$, in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal~$B(\lambda)$, in terms of the marginally large tableaux, for the $G_2$ Lie algebra type. We also provide a new description of $B(\la)$, in terms of Nakajima monomials, that is in natural correspondence with our tableau description.
Keywords: crystal base, $G_2$ type Lie algebra, marginally large tableau, Nakajima monomial
MSC numbers: 17B37, 81R50
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