Stuttering blocks of Ariki–Koike algebras

Blocs bégayants des algèbres d'Ariki–Koike

Salim Rostam (1)

1 LMV - Laboratoire de Mathématiques de Versailles

We study a shift action defined on multipartitions and on residue multisets of their Young diagrams. We prove that the minimal orbit cardinality among all multipartitions associated to a given multiset depends only on the orbit cardinality of the multiset. Using abaci, this problem reduces to a convex optimisation problem over the integers with linear constraints. We solve it by proving an existence theorem for binary matrices with prescribed row, column and block sums. Finally, we give some applications to the representation theory of the Hecke algebra of the complex reflection group G(r,p,n).

Mots clés: Residues; Abacus; Hecke algebras; Ariki-Koike algebras; Multipartitions

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

Salim Rostam. Stuttering blocks of Ariki–Koike algebras. 2018. ⟨hal-01794943v1⟩