Canonical basic sets in type B

Meinolf Geck (1) , Nicolas Jacon (2)

1 ABE - Department of Mathematical Sciences
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

More than 10 years ago, Dipper, James and Murphy developped the theory of Specht modules for Hecke algebras of type $B_n$. More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrisations of the irreducible representations of Hecke algebras (of any finite type) in terms of so-called canonical basic sets. For certain values of the parameters in type $B_n$, combinatorial descriptions of these basic sets were found by Jacon, based on work of Ariki and Foda-Leclerc-Okado-Thibon-Welsh. Here, we consider the canonical basic sets for all the remaining choices of the parameters.

Mots clés: Lusztig's a fonction; Hecke algebras; modular representations; Lusztig's a fonction.

Domaines: Théorie des représentations [math.RT]

Meinolf Geck, Nicolas Jacon. Canonical basic sets in type B. Journal of Algebra, 2006, 306, pp.104-127. ⟨hal-00016536v2⟩