Double Yangians and lattice quantum vertex algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912595930251264 |
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| author | Kong, Fei Li, Haisheng |
| author_facet | Kong, Fei Li, Haisheng |
| contents | For any simply-laced GCM $A$, a $\mathbb C[[\hbar]]$-algebra $\widehat{\mathcal{DY}}(A)$ was introduced in [KL1], where it was proved that the universal vacuum $\widehat{\mathcal{DY}}(A)$-module ${\mathcal{V}}_A(\ell)$ for any fixed level $\ell$ is naturally an $\hbar$-adic weak quantum vertex algebra. Let $L$ be the root lattice of $\mathfrak g(A)$. As the main results of this paper, we construct an $\hbar$-adic quantum vertex algebra $V_L[[\hbar]]^η$ as a formal deformation of the lattice vertex algebra $V_L$ and show that every $V_L[[\hbar]]^η$-module is naturally a restricted $\widehat{\mathcal{DY}}(A)$-module of level one. For $A$ of finite type, we obtain a realization of $V_L[[\hbar]]^η$ as a quotient of the $\hbar$-adic weak quantum vertex algebra ${\mathcal{V}}_A(1)$, giving a characterization of $V_L[[\hbar]]^η$-modules as restricted $\widehat{\mathcal{DY}}(A)$-modules of level one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Double Yangians and lattice quantum vertex algebras Kong, Fei Li, Haisheng Quantum Algebra For any simply-laced GCM $A$, a $\mathbb C[[\hbar]]$-algebra $\widehat{\mathcal{DY}}(A)$ was introduced in [KL1], where it was proved that the universal vacuum $\widehat{\mathcal{DY}}(A)$-module ${\mathcal{V}}_A(\ell)$ for any fixed level $\ell$ is naturally an $\hbar$-adic weak quantum vertex algebra. Let $L$ be the root lattice of $\mathfrak g(A)$. As the main results of this paper, we construct an $\hbar$-adic quantum vertex algebra $V_L[[\hbar]]^η$ as a formal deformation of the lattice vertex algebra $V_L$ and show that every $V_L[[\hbar]]^η$-module is naturally a restricted $\widehat{\mathcal{DY}}(A)$-module of level one. For $A$ of finite type, we obtain a realization of $V_L[[\hbar]]^η$ as a quotient of the $\hbar$-adic weak quantum vertex algebra ${\mathcal{V}}_A(1)$, giving a characterization of $V_L[[\hbar]]^η$-modules as restricted $\widehat{\mathcal{DY}}(A)$-modules of level one. |
| title | Double Yangians and lattice quantum vertex algebras |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2509.16592 |