Crystal isomorphisms for irreducible highest weight U_{v}{\hat{sl}}_{e})-modules of higher level

We study the crystal graphs of irreducible U_{v}(\hat{sl}}_{e})-modules of higher level l. Generalizing works of the first author, we obtain a simple description of the bijections between the classes of multipartitions which naturally label these graphs: the Uglov multipartitions. This is achieved by expliciting an embedding of the U_{v}(\hat{sl}}_{e})-crystals of level l into $U_v({\widehat{sl}}_{\mathrm{\infty }})$-crystals associated to highest weight modules.