This is a question about the second point in Geordie Williamson's answer in 

http://mathoverflow.net/questions/138310/what-to-do-now-that-lusztigs-and-james-conjectures-have-been-shown-to-be-false/146408#146408
,

which says that the Lusztig conjecture for quantum groups at a $p$-th root of unity doesn't need $p\geq h$. I only have heard of the conjecture and proof about the regular block, which requires $p\geq h$. Of course, if there exists a regular block, translating shows that a singular block has character formula with parabolic KL polynomials. But how do you get the result for the $p<h$ case? Does it use the KL correspondence to the affine Lie algebra? Is there any place I can see this explained?