Crystal Graphs of Higher Level q-deformed Fock Spaces, Lusztig a-values and Ariki–Koike Algebras
We show that the different labelings of the crystal graph for irreducible highest weight $\mathcal{U}_q (\widehat{\mathfrak{sl}}_e)$-modules lead to different labelings of the simple modules for non semisimple Ariki–Koike algebras by using Lusztig a-values.