CRYSTAL B(λ) IN B(∞) FOR G₂TYPE LIE ALGEBRA
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A previous work gave a combinatorial description of the crys- tal B(∞), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Us- ing this result, we present an explicit description of the crystal B(λ), in terms of the marginally large tableaux, for the G₂Lie algebra type. We also provide a new description of B(λ), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.
Abstract
A previous work gave a combinatorial description of the crys- tal B(∞), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Us- ing this result, we present an explicit description of the crystal B(λ), in terms of the marginally large tableaux, for the G₂Lie algebra type. We also provide a new description of B(λ), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.
참고문헌 (21)
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