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arXiv · 2509.16528

Double Yangians and quantum vertex algebras, I

Fei Kong·Haisheng Li
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Abstract

For any symmetrizable generalized Cartan matrix $A$, we introduce an algebra $\widehat{\mathcal{DY}}(A)$, which is essentially the centrally extended double Yangian when $A$ is of finite type, and we give a new field (current) presentation of $\widehat{\mathcal{DY}}(A)$. Among the main results, for any $\ell\in \mathbb C$ we construct a universal vacuum $\widehat{\mathcal{DY}}(A)$-module $\mathcal{V}_A(\ell)$ of level $\ell$, prove that there exists a natural $\hbar$-adic weak quantum vertex algebra structure on $\mathcal{V}_A(\ell)$, and give an isomorphism between the category of restricted $\widehat{\mathcal{DY}}(A)$-modules of level $\ell$ and the category of $\mathcal{V}_A(\ell)$-modules.

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Fei Kong, Haisheng Li. 2025-09-20. Double Yangians and quantum vertex algebras, I. https://arxiv.org/abs/2509.16528

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