Quantum Affine Vertex Algebras Associated to Untwisted Quantum Affinization Algebras

Let U-h((g) over cap) be the untwisted affinization of a symmetrizable quantum Kac-Moody algebra U-h((g) over cap). For l ? C, we construct an h-adic quantum vertex algebra V-(g) over cap ,V-h (l, 0), and establish a one-to-one correspondence between 0-coordinated V-(g) over cap ,V-h(l, 0)- modules and restricted U-h((g) over cap)-modules of level l. Suppose that l is a positive integer. We construct a quotient h-adic quantum vertex algebra L-(g) over cap ,L-h (l, 0) of V-(g) over cap ,V-h(l, 0), and es-tablish a one-to-one correspondence between certain 0-coordinated L-(g) over cap ,L-h (l, 0)-modules and restricted integrable U-h((g) over cap)-modules of level l. Suppose further that g is of finite type. We prove that L-(g) over cap ,L-h(l, 0)/hL((g) over cap ,h)(l, 0) is isomorphic to the simple affine vertex algebra L-(g) over cap(l, 0).