On the one dimensional representations of Ariki-Koike algebras at roots of unity

Nicolas Jacon (1)

1 LMR - Laboratoire de Mathématiques de Reims

We study the natural labeling of the one dimensional representations for Ariki-Koike algebras at roots of unity. For Hecke algebras of types A and B, some of these representations can be identified with the socle of the Steinberg representation of a finite reductive group. We here give closed formulas for them. This uses, in particular, several results concerning crystal isomorphisms and the Mullineux involution.

Domaines: Théorie des représentations [math.RT]; Combinatoire [math.CO]

Nicolas Jacon. On the one dimensional representations of Ariki-Koike algebras at roots of unity. Journal of Pure and Applied Algebra, 2017, 21 (7), ⟨10.1016/j.jpaa.2016.09.012⟩. ⟨hal-01197065⟩