On the Mullineux involution for Ariki-Koike algebras

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

This note is concerned with a natural generalization of the Mullineux involution for Ariki-Koike algebras. Using a result of Fayers together with previous results by the authors, we give an efficient algorithm for computing this generalized Mullineux involution. Our algorithm notably does not involve the determination of paths in affine crystals.

Mots clés: crystal graph

Mots clés: Ariki-Koike algebras; Mullineux involution; crystal graph.

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

Nicolas Jacon, Cédric Lecouvey. On the Mullineux involution for Ariki-Koike algebras. Journal of Algebra, 2009, 321 (No. 8), pp.2156-2170. ⟨hal-00269840v3⟩