Canonical basic sets in type B

23 pages, minor changes.International audienceMore 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