2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101204We show that the different labelings of the crystal graph for irreducible highest weight $\mathcal{U}\_q (\hat{\mathfrak{sl}}\_e)$-modules lead to different labelings of the simple modules for non semisimple Ariki-Koike algebras by using Lusztig $a$-values.Representation TheoryQuantum Algebra20C08;17B37Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebrastext