Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebras

Nicolas Jacon (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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.

Mots clés: Ariki-Koike algebras; Fock spaces.; Fock spaces

Domaines: Théorie des représentations [math.RT]; Algèbres quantiques [math.QA]

Nicolas Jacon. Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebras. Algebras and Representation Theory, 2007, 10 (6), pp.565-591. ⟨hal-00004683v3⟩