Associated varieties of simple affine VOAs $L_k(sl_3)$ and $W$-algebras $W_k(sl_3,f)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917976953847808 |
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| author | Jiang, Cuipo Song, Jingtian |
| author_facet | Jiang, Cuipo Song, Jingtian |
| contents | In this paper we first prove that the maximal ideal of the universal affine vertex operator algebra $V^k(sl_n)$ for $k=-n+\frac{n-1}{q}$ is generated by two singular vectors of conformal weight $3q$ if $n=3$, and by one singular vector of conformal weight $2q$ if $n\geq 4$. We next determine the associated varieties of the simple vertex operator algebras $L_k(sl_3)$ for all the non-admissible levels $k=-3+\frac{2}{2m+1}$, $m\geq 0$. The varieties of the associated simple affine $W$-algebras $W_k(sl_3,f)$, for nilpotent elements $f$ of $sl_3$, are also determined. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_03552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Associated varieties of simple affine VOAs $L_k(sl_3)$ and $W$-algebras $W_k(sl_3,f)$ Jiang, Cuipo Song, Jingtian Quantum Algebra Representation Theory 17B67, 17B69 In this paper we first prove that the maximal ideal of the universal affine vertex operator algebra $V^k(sl_n)$ for $k=-n+\frac{n-1}{q}$ is generated by two singular vectors of conformal weight $3q$ if $n=3$, and by one singular vector of conformal weight $2q$ if $n\geq 4$. We next determine the associated varieties of the simple vertex operator algebras $L_k(sl_3)$ for all the non-admissible levels $k=-3+\frac{2}{2m+1}$, $m\geq 0$. The varieties of the associated simple affine $W$-algebras $W_k(sl_3,f)$, for nilpotent elements $f$ of $sl_3$, are also determined. |
| title | Associated varieties of simple affine VOAs $L_k(sl_3)$ and $W$-algebras $W_k(sl_3,f)$ |
| topic | Quantum Algebra Representation Theory 17B67, 17B69 |
| url | https://arxiv.org/abs/2409.03552 |