2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118077This dissertation addresses several current problems in Representation Theory using crystal bases. It incorporates the results of arXiv:math.QA/0408113 and arXiv:math.RT/0603547, as well as previously unpublished results.Quantum AlgebraRepresentation Theory05E99 (Primary), 17B37, 81R10 (Secondary)text