In this talk I will present my recent joint work with Bin Xu on a conjecture of Geiss-Leclerc-Schr{\"o}er, which is an analogue of a classical conjecture of Lusztig in the Weyl group case. It concerns the relation between canonical basis and semi-canonical basis through the characteristic cycles. I will explain  our approach to this conjecture  and how to reduce the conjecture to show that certain nearby cycles have vanishing Euler characteristic.