Abstract
AbstractNakajima introduced a certain set of monomials realizing the irreducible highest weight crystalsB(λ). The monomial set can be extended so that it contains crystalB(∞) in addition toB(λ). We present explicit descriptions of the crystalsB(∞) andB(λ) over special linear Lie algebras in the language of extended Nakajima monomials. There is a natural correspondence between the monomial description and Young tableau realization, which is another realization of crystalsB(∞) andB(λ).
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