Symmetric quiver varieties and critical stable envelopes
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911356404367360 |
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| author | Cao, Yalong Okounkov, Andrei Zhou, Yehao Zhou, Zijun |
| author_facet | Cao, Yalong Okounkov, Andrei Zhou, Yehao Zhou, Zijun |
| contents | Symmetric quiver varieties with potentials are natural generalizations of Nakajima quiver varieties, and their equivariant critical cohomologies provide more flexible settings for geometric representation theory and enumerative geometry. In this paper, we study their geometric properties and show that they behave like universally deformed Nakajima quiver varieties. Based on this, we provide a new proof of the existence of critical stable envelopes on them. Following an idea of Nakajima, we give a sheaf theoretic interpretation of critical stable envelopes by the hyperbolic restriction in the affinization of symmetric quiver varieties. The associativity of hyperbolic restrictions implies the triangle lemma of critical stable envelopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02719 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetric quiver varieties and critical stable envelopes Cao, Yalong Okounkov, Andrei Zhou, Yehao Zhou, Zijun Algebraic Geometry High Energy Physics - Theory Mathematical Physics Representation Theory 14D20, 16G20 (Primary) 17B37 (Secondary) Symmetric quiver varieties with potentials are natural generalizations of Nakajima quiver varieties, and their equivariant critical cohomologies provide more flexible settings for geometric representation theory and enumerative geometry. In this paper, we study their geometric properties and show that they behave like universally deformed Nakajima quiver varieties. Based on this, we provide a new proof of the existence of critical stable envelopes on them. Following an idea of Nakajima, we give a sheaf theoretic interpretation of critical stable envelopes by the hyperbolic restriction in the affinization of symmetric quiver varieties. The associativity of hyperbolic restrictions implies the triangle lemma of critical stable envelopes. |
| title | Symmetric quiver varieties and critical stable envelopes |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics Representation Theory 14D20, 16G20 (Primary) 17B37 (Secondary) |
| url | https://arxiv.org/abs/2601.02719 |