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

Nicolas Jacon (1) , Cédric Lecouvey (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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 $U_{v}(\hat{sl}_{\infty })$-crystals associated to highest weight modules.

Domaines: Théorie des représentations [math.RT]

Nicolas Jacon, Cédric Lecouvey. Crystal isomorphisms for irreducible highest weight $U_{v}{\hat{sl}}_{e})$-modules of higher level. Algebras and Representation Theory, 2010, 13, pp.467-489. ⟨hal-00151866v2⟩