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

Nicolas Jacon (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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: Foxk spaces.

Mots clés: Ariki-Koike algebras; Foxk 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. 2005. ⟨hal-00004683v1⟩