Canonical basic sets in type Bn

More than 10 years ago, Dipper, James and Murphy developed the theory of Specht modules for Hecke algebras of type Bn. More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrizations 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 Bn, 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.