The characteristic cycles and semi-canonical bases on type A quiver variety
Abstract
In this article we study a conjecture of Geiss-Leclerc-Schr\"oer, 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 A2 quiver. In general type A case, we reduce the conjecture to show that certain nearby cycles have vanishing Euler characteristic.
0