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The singular-support characterization of Lusztig sheaves

A mix of human-written and AI-generated textHuman understanding: some partsmath.RT — Representation Theorymath.AG — Algebraic Geometry

Contributed by Qiyue Tang ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

Abstract

We prove that for every finite loop-free quiver and every dimension vector, a simple equivariant perverse sheaf with complex coefficients on the quiver representation space is a Lusztig sheaf if and only if its singular support lies in Lusztig’s nilpotent variety.

Provenance statement

GPT-6-Pro was used to develop the proof during a two-hour research run. Codex was used to review the proof and revise the manuscript. A review using Rethlas-OSV is planned, and its results will be reported in a later revision.

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Version history

  1. v1 · 22 pagesSubmitted by Qiyue TangInitial depositCurrentNov 07, 2026