Does anyone know a reference for the construction of cell modules for the Weyl group of type $D$, without any reference to the Weyl group of type $B$?

What would be even better is an idempotent construction along the lines of: take the product of the row and column stabilisers of the partition (as in the type $A$ case) with some other idempotent (as in the type $B$ case).

Thanks!