CRYSTAL B(λ) IN B(∞) FOR G2 TYPE LIE ALGEBRA

Title & Authors
CRYSTAL B(λ) IN B(∞) FOR G2 TYPE LIE ALGEBRA
Kim, Min Kyu; Lee, Hyeonmi;

Abstract
A previous work gave a combinatorial description of the crystal B($\small{{\infty}}$), 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($\small{{\lambda}}$), in terms of the marginally large tableaux, for the $\small{G_2}$ Lie algebra type. We also provide a new description of B($\small{{\lambda}}$), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.
Keywords
crystal base;$\small{G_2}$ type Lie algebra;marginally large tableau;Nakajima monomial;
Language
English
Cited by
1.
Crystal ℬ ( λ ) $\mathcal {B}(\lambda )$ as a Subset of the Tableau Description of ℬ ( ∞ ) $\mathcal {B}(\infty )$ for the Classical Lie Algebra Types, Algebras and Representation Theory, 2015, 18, 1, 137
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