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Apr 13, 2013 at 20:12 comment added Ben Webster Mmm, not sure about that; I never really read that book. You should also be able to use the projective $P(w_0w)$ in place of the tilting $T(w)$; for some reason tilting modules felt better when I was writing the answer, but there's a functor that switches projectives and tiltings and induces the isomorphism $P(w_0)=T(e)$ so its essentially the same story.
Apr 13, 2013 at 19:41 vote accept George Melvin
Apr 13, 2013 at 19:41 comment added George Melvin Excellent, thanks for your comments. I'll have a think about this. I take it that it will suffice to have a look in Humphreys's 'Category O' for the tilting module material?
Apr 13, 2013 at 19:04 history edited Ben Webster CC BY-SA 3.0
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Apr 13, 2013 at 18:59 history answered Ben Webster CC BY-SA 3.0