Specht modules and Kazhdan-Lusztig cells in type B_n

Dipper, James and Murphy generalized the classical Specht module theory to Hecke
algebras of type Bn. On the other hand, for any choice of a monomial order on the parameters in type Bn, we obtain corresponding Kazhdan–Lusztig cell modules. In this paper, we show that the Specht modules are naturally isomorphic to the Kazhdan–Lusztig cell modules if we choose the dominance order on the parameters, as in the “asymptotic case” studied by Bonnaf´e and the second named author. We also give examples which show that such an isomorphism does not exist
for other choices of monomial orders.