2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101339We present explicit descriptions of the crystals $\mathcal{B}(\infty)$ and $\mathcal{B}(λ)$ over special linear Lie algebras in the language of \emph{extended Nakajima monomials}. There is a natural correspondence between the monomial description and Young tableau realization, which is another realization of crystals $\mathcal{B}(\infty)$ and $\mathcal{B}(λ)$.20 pagesQuantum AlgebraRepresentation Theory17B37, 81R50text