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Rouquier blocks of the cyclotomic Ariki-Koike algebras

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2008

Résumé

The definition of Rouquier for families of characters of Weyl groups in terms of blocks of the associated Iwahori-Hecke algebra has made possible the generalization of this notion to the complex reflection groups. Here we give an algorithm for the determination of the "Rouquier blocks" of the cyclotomic Ariki-Koike algebras.

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https://infoscience.epfl.ch/entities/publication/53ab2c29-6eba-42d7-9c60-93e931a69a1d

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Concepts associés (12)

Groupe de Coxeter

Un groupe de Coxeter est un groupe engendré par des réflexions sur un espace. Les groupes de Coxeter se retrouvent dans de nombreux domaines des mathématiques et de la géométrie. En particulier, les groupes diédraux, ou les groupes d'isométries de polyèdres réguliers, sont des groupes de Coxeter. Les groupes de Weyl sont d'autres exemples de groupes de Coxeter. Ces groupes sont nommés d'après le mathématicien H.S.M. Coxeter. Un groupe de Coxeter est un groupe W ayant une présentation du type: où est à valeurs dans , est symétrique () et vérifie , si .

Reflection group

In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent copies of a regular polytope is necessarily a reflection group. Reflection groups also include Weyl groups and crystallographic Coxeter groups. While the orthogonal group is generated by reflections (by the Cartan–Dieudonné theorem), it is a continuous group (indeed, Lie group), not a discrete group, and is generally considered separately.

Complex reflection group

In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise. Complex reflection groups arise in the study of the invariant theory of polynomial rings. In the mid-20th century, they were completely classified in work of Shephard and Todd. Special cases include the symmetric group of permutations, the dihedral groups, and more generally all finite real reflection groups (the Coxeter groups or Weyl groups, including the symmetry groups of regular polyhedra).

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