Ribbon tableaux, ribbon rigged configurations and Hall-Littlewood functions at roots of unity

Francois Descouens (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using A. Schilling's bijection between ribbon tableaux and ribbon rigged configurations.

Mots clés: Ribbon tableaux; Rigged configurations; Hall-Littlewood functions

Domaines: Combinatoire [math.CO]; Algèbres quantiques [math.QA]

Francois Descouens. Ribbon tableaux, ribbon rigged configurations and Hall-Littlewood functions at roots of unity. 2007. ⟨hal-00123035v2⟩