The Kazhdan-Lusztig category of W-algebras of simply-laced Lie algebras at irrational levels
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912943216525312 |
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| author | Creutzig, Thomas Dhillon, Gurbir Nakatsuka, Shigenori |
| author_facet | Creutzig, Thomas Dhillon, Gurbir Nakatsuka, Shigenori |
| contents | Let $\mathfrak{g}$ be a simple, simply-laced Lie algebra and $f \in \mathfrak{g}$ nilpotent. The Kazhdan-Lusztig category of the W-algebra $W^κ(\mathfrak{g},f)$ associated with $(\mathfrak{g},f)$ at level $κ\in \mathbb{C}$ is obtained from the Kazhdan-Lusztig category of the affine vertex algebra $V^κ(\mathfrak{g})$ via the quantum Hamiltonian reduction associated with $f$. We show that this is a braided tensor equivalence for any $f$ and any irrational level $κ\in \mathbb{C} \backslash \mathbb{Q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04667 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Kazhdan-Lusztig category of W-algebras of simply-laced Lie algebras at irrational levels Creutzig, Thomas Dhillon, Gurbir Nakatsuka, Shigenori Representation Theory Let $\mathfrak{g}$ be a simple, simply-laced Lie algebra and $f \in \mathfrak{g}$ nilpotent. The Kazhdan-Lusztig category of the W-algebra $W^κ(\mathfrak{g},f)$ associated with $(\mathfrak{g},f)$ at level $κ\in \mathbb{C}$ is obtained from the Kazhdan-Lusztig category of the affine vertex algebra $V^κ(\mathfrak{g})$ via the quantum Hamiltonian reduction associated with $f$. We show that this is a braided tensor equivalence for any $f$ and any irrational level $κ\in \mathbb{C} \backslash \mathbb{Q}$. |
| title | The Kazhdan-Lusztig category of W-algebras of simply-laced Lie algebras at irrational levels |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2603.04667 |