Cellular structures on Hecke algebras of type B

Cédric Bonnafé (1) , Nicolas Jacon (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

The aim of this paper is to gather and (try to) unify several approaches for the modular representation theory of Hecke algebras of type $B$. We attempt to explain the connections between Geck's cellular structures (coming from Kazhdan-Lusztig theory with unequal parameters) and Ariki's Theorem on the canonical basis of the Fock spaces.

Mots clés: Kazhdan-Lusztig theory; Hecke algebras; modular representation; cellular algebras; Kazhdan-Lusztig theory.

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

Cédric Bonnafé, Nicolas Jacon. Cellular structures on Hecke algebras of type B. Journal of Algebra, 2009, 321 (11), pp.3089-3111. ⟨10.1016/j.jalgebra.2008.04.017⟩. ⟨hal-00200588v3⟩