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On singular supports of Lusztig's perverse sheaves (2401.02770v1)
Published 5 Jan 2024 in math.RT, math.AG, and math.QA
Abstract: We prove a conjecture of Lusztig on a microlocal characterization of his perverse sheaves. For any finite quiver without loops, an equivariant simple perverse sheaf on the variety of quiver representations is a Lusztig's perverse sheaf if and only if its singular support is contained in Lusztig's Lagrangian variety, that is, the variety of nilpotent representations of the preprojective algebra of the quiver.