CRYSTAL B(λ) IN B(∞) FOR G2TYPE LIE ALGEBRA

Abstract

A previous work gave a combinatorial description of the crystal B(<TEX>${\infty}$</TEX>), 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(<TEX>${\lambda}$</TEX>), in terms of the marginally large tableaux, for the <TEX>$G_2$</TEX> Lie algebra type. We also provide a new description of B(<TEX>${\lambda}$</TEX>), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.