Filtration and gradation of quantum affine vertex algebras

Abstract

In this paper, we present a unified construction of quantum affine vertex algebras associated to double Yangians, untwisted quantum affinization algebras, and twisted quantum affinization algebras. We show that these $\hslash$-adic quantum vertex algebras contain a dense quantum vertex subalgebra equipped with a increasing filtration. Moreover, we prove that the associated graded algebras with respect to these filtrations are isomorphic to a $\mathbb{Z}$-graded dense quantum vertex subalgebra of the quantum affine vertex algebras associated to double Yangians.