What I said is Lusztig's conjecture about representation of quantum group at root of unity and representation of Lie algebra at positive characters.


It seems that Andersen-Jantzen-Soergel ever wrote a book on this conjecture. 


Is it solved? Any recent development? I am looking for reference talking about it. 


Thank you 



Is Lusztig's conjecture solved?
The result of that book is that the conjecture is true for sufficiently large, but unspecified characteristic. (First fix a Dynkin type.)
More recently Peter Fiebig has given actual bounds. See


An upper bound on the exceptional characteristics for Lusztig's character formula
by Peter Fiebig arXiv:0811.1674v2 at <http://arxiv.org/pdf/0811.1674v2>


