Crystal $\Bla$ in $B(\infty )$ for $G_2$ type Lie Algebra

Abstract

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.

13 pages, submitted

References in corpus (1)

• Young tableaux, canonical bases and the Gindikin-Karpelevich formula