2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77047We give a general way of representing the crystal (base) corresponding to the intgrable highest weight modules of quantum Kac-Moody algebras, which is called polyhedral realizations. This is applied to describe explicitly the crystal bases of integrable highest weight modules for arbitrary rank 2 Kac-Moody algebra cases, the classical A_n-case and the affine A^{(1)}_{n-1}-case.LaTeX, 27 pages, some reference is addedQuantum AlgebraCombinatoricsRepresentation Theorytext