Handsaw quiver varieties and finite $W$-algebras

Abstract: Following Braverman-Finkelberg-Fegin-Rybnikov (arXiv:1008.3655), we study the convolution algebra of handsaw quiver varieties, a.k.a. Laumon spaces, and finite $W$-algebras of type $A$. A new observation is that their simple modules are described in terms of IC sheaves of graded quiver varieties of type $A$, which were known to be related to Kazhdan-Lusztig polynomials of type $A$. This confirms a conjecture by Brundan-Kleshchev.