Quantum Affine Vertex Algebras Associated to Untwisted Quantum Affinization Algebras

Let $\mathcal U_\hbar(\hat{\mathfrak g})$ be the untwisted quantum affinization of a symmetrizable Kac-Moody algebra U_\hbar({\mathfrak g})$. For $\ell\in\mathbb C$, we construct an $\hbar$-adic vertex $V_{\hat{\mathfrak g},\hbar}(\ell,0)$, and establish one-to-one correspondence between $\phi$-coordinated g},\hbar}(\ell,0)$-modules restricted g})$-modules level $\ell$. Suppose that $\ell$ is positive integer. We quotient $L_{\hat{\mathfrak g},\hbar}(\ell,0)$ certain integrable further ${\mathfrak g}$ finite type. prove g},\hbar}(\ell,0)/\hbar L_{\hat{\mathfrak isomorphic to simple affine g}}(\ell,0)$.