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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.04445 |
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| _version_ | 1866908632241668096 |
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| author | Jiang, Cuipo Song, Jingtian |
| author_facet | Jiang, Cuipo Song, Jingtian |
| contents | Given a finite-dimensional complex simple Lie algebra $\mathfrak{g}$ and a complex number $κ$, let $V^κ(\mathfrak{g})$ be the associated universal affine vertex algebra. In [GK07], the authors gave a sufficient and necessary condition for $V^κ(\mathfrak{g})$ to be simple. In this paper, we determine the weights of singular vectors of $V^κ(\mathfrak{g})$ with minimal conformal weights, when $\mathfrak{g}$ is simply-laced and $V^κ(\mathfrak{g})$ is not simple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On singular vectors of simply-laced universal affine vertex operator algebras Jiang, Cuipo Song, Jingtian Quantum Algebra Given a finite-dimensional complex simple Lie algebra $\mathfrak{g}$ and a complex number $κ$, let $V^κ(\mathfrak{g})$ be the associated universal affine vertex algebra. In [GK07], the authors gave a sufficient and necessary condition for $V^κ(\mathfrak{g})$ to be simple. In this paper, we determine the weights of singular vectors of $V^κ(\mathfrak{g})$ with minimal conformal weights, when $\mathfrak{g}$ is simply-laced and $V^κ(\mathfrak{g})$ is not simple. |
| title | On singular vectors of simply-laced universal affine vertex operator algebras |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2510.04445 |