On singular supports of Lusztig's perverse sheaves
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916081504878592 |
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| author | Fang, Jiepeng |
| author_facet | Fang, Jiepeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02770 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On singular supports of Lusztig's perverse sheaves Fang, Jiepeng Representation Theory Algebraic Geometry Quantum Algebra 14F08, 16G20, 17B37 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. |
| title | On singular supports of Lusztig's perverse sheaves |
| topic | Representation Theory Algebraic Geometry Quantum Algebra 14F08, 16G20, 17B37 |
| url | https://arxiv.org/abs/2401.02770 |