Advances in Mathematics (2015) 772-807.

I prove that Lusztig’s conjecture reduces to a problem about the light leaves (as defined in my first paper). Using the result in Section 4.3 of this paper Geordie Williamson disproved Lusztig’s conjecture! The counterexamples grow exponentially in the Coxeter number. Here is Geordie’s paper

PDF Light leaves and Lusztig’s conjecture