Taiwang DengYau Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing, 100084, ChinaBin XuYau Mathematical Sciences Center and Department of Mathematics, Tsinghua University, Beijing, China
In this article we study a conjecture of Geiss-Leclerc-Schröer, 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. We formulate an approach to this conjecture and prove it for type quiver. In the general type A case, we reduce the conjecture to show that certain nearby cycles have vanishing Euler characteristic.