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Aug 13, 2017 at 23:20 comment added Ben Webster I really mean dominant (all coroots are positive) and anti-dominant (all are negative).
Aug 11, 2017 at 15:33 comment added Antoine What definition of dominant are you using here ? Is it $\Lambda^+$ (the $\mathbb{Z}^+$ span of the fundamental weights) or $\Lambda^+ - \rho$ ?
Aug 3, 2017 at 11:13 comment added Antoine Thanks for the answer! You say the answer is different for singular blocks, can you say more about it (or give a reference)?
Aug 3, 2017 at 11:12 vote accept Antoine
Aug 2, 2017 at 17:24 comment added Jim Humphreys Concerning non-integral weights, see my comments and references in 8.8. Though Kazhdan-Lusztig apparently didn't go into this, the non-integral case was later filled in by Soergel and generalized in the work of Kashiwara-Tanisaki for Kac-Moody Lie algebras.
Aug 2, 2017 at 15:56 history answered Ben Webster CC BY-SA 3.0