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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!

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The term "cell module" is a bit vague. I assume you want the Kazhdan-Lusztig-Cells (as opposed to say the cell modules that come from a cellular basis of the Hecke algebra) ? Then I don't think that there will be a nice description in terms of partitions because the KL-cells are in general not irreducible for type D. This means that there are fewer of them then there are irreducibles. –  Johannes Hahn Apr 29 '12 at 14:28
    
Oops. No, I just want a basis of the "Specht modules" - or cellular basis of the Hecke algebra (at q=1). –  Chris Bowman Apr 30 '12 at 7:42
    
@Chris: It would also be helpful to provide some context with a reference to the literature you've already looked at. –  Jim Humphreys May 1 '12 at 13:15
    
I've mostly been reading the work of Ariki, Mathas, Hu, Ram, Michel, and Marin. It seems that there is no easy construction (without reference to the type B case). I've since been told that the only place I'm likely to find an "internal construction" of the "Specht" modules is in Gecke's paper "Hecke algebras of finite type are cellular". –  Chris Bowman May 1 '12 at 18:31
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