Microlocal characterization of Lusztig sheaves for affine quivers and $g$-loops quivers

Abstract

We prove that for extended Dynkin quivers, simple perverse sheaves in Lusztig category are characterized by the nilpotency of their singular support. This proves a conjecture of Lusztig in the case of affine quivers. For cyclic quivers, we prove a similar result for a larger nilpotent variety and a larger class of perverse sheaves. We formulate conjectures for similar results for quivers with loops, for which we have to use the appropriate notion of nilpotent variety, due to Bozec, Schiffmann and Vasserot. We prove our conjecture for $g$-loops quivers ($g\ge 2$).

Comments welcome! Contains appendices with basics of microlocal theory of constructible sheaves. The new version contains a remark explaining how to obtain a alternative proof of the first main theorem of the paper using the theory of quantized symplectic resolutions

Cited by in corpus (1)

• Perverse sheaves with nilpotent singular support on the stack of coherent sheaves on an elliptic curve