2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70425We describe the crystal bases of the modified quantum algebras and give the explicit form of the highest (or lowest) weight vector of its connected component $B_0(λ)$ containing the unit element for arbitrary rank 2 cases. We also present the explicit form of $B_0(λ)$ containing the highest (or lowest) weight vector by the polyhedral realization method.26 pages, LaTeXQuantum AlgebraRepresentation Theorytext