Quantization of parafermion vertex algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908619273928704 |
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| author | Kong, Fei |
| author_facet | Kong, Fei |
| contents | Let $\mathfrak g$ be a finite dimensional simple Lie algebra over $\mathbb C$, and let $\ell$ be a positive integer. In this paper, we construct the quantization $K_{\hat{\mathfrak g},\hbar}^\ell$ of the parafermion vertex algebra $K_{\hat{\mathfrak g}}^\ell$ as an $\hbar$-adic quantum vertex subalgebra inside the simple quantum affine vertex algebra $L_{\hat{\mathfrak g},\hbar}^\ell$. We show that $L_{\hat{\mathfrak g},\hbar}^\ell$ contains an $\hbar$-adic quantum vertex subalgebra isomorphic to the quantum lattice vertex algebra $V_{\sqrt\ell Q_L}^{η_\ell}$, where $Q_L$ is the lattice generated by the long roots of ${\mathfrak g}$. Moreover, we prove the double commutant property of $K_{\hat{\mathfrak g},\hbar}^\ell$ and $V_{\sqrt\ell Q_L}^{η_\ell}$ in $L_{\hat{\mathfrak g},\hbar}^\ell$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03571 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantization of parafermion vertex algebras Kong, Fei Quantum Algebra 17B69 Let $\mathfrak g$ be a finite dimensional simple Lie algebra over $\mathbb C$, and let $\ell$ be a positive integer. In this paper, we construct the quantization $K_{\hat{\mathfrak g},\hbar}^\ell$ of the parafermion vertex algebra $K_{\hat{\mathfrak g}}^\ell$ as an $\hbar$-adic quantum vertex subalgebra inside the simple quantum affine vertex algebra $L_{\hat{\mathfrak g},\hbar}^\ell$. We show that $L_{\hat{\mathfrak g},\hbar}^\ell$ contains an $\hbar$-adic quantum vertex subalgebra isomorphic to the quantum lattice vertex algebra $V_{\sqrt\ell Q_L}^{η_\ell}$, where $Q_L$ is the lattice generated by the long roots of ${\mathfrak g}$. Moreover, we prove the double commutant property of $K_{\hat{\mathfrak g},\hbar}^\ell$ and $V_{\sqrt\ell Q_L}^{η_\ell}$ in $L_{\hat{\mathfrak g},\hbar}^\ell$. |
| title | Quantization of parafermion vertex algebras |
| topic | Quantum Algebra 17B69 |
| url | https://arxiv.org/abs/2310.03571 |